: Why is character lifetime proportional to character development so often? Hollywood movies are a good example of this, but also many books feature the rule. When the plot revolves around life

I call this the "anthropic principle of fiction", based loosely on the actual anthropic principle.

Loosely speaking, the anthropic principle states that it's no coincidence that we happen to be found in a state where sentient life exists, because that's the only state in which there are people who can ask "how did we get to a place where sentient life exists?" (For example, there's no sense in which we're lucky to be born on Earth instead of Mars or Mercury, because, out of the three, we only could have been born on Earth.)

Similarly, suppose some set of events happen in a fictional world that warrants a book. That book will cover the experiences of some people. Some people in this fictional event didn't survive long enough for there to be a whole book about them. So it's no coincidence that the ones you're reading about in the book you picked off the shelf were the ones who survived long enough to have their exploits covered by a book.

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All good answers so far. Let me add one concept that helps me:

History is written by the victors.

Everyone is the hero of their own story. All those people who died along the way did not survive to tell their stories. That's why the protagonist/narrator survives. If he hadn't survived, we would have gone to someone else to relate the events in question.

Imagine a news story which is later made into a book. The reporter interviews eyewitnesses and survivors. When it comes time to write the book, those people's views and experiences will disproportionately affect the final product.

The survivor determines which events are most meaningful, and the people who most impacted those events might have larger parts in the narrator/survivor's mind. Also, the people who either impacted or continue to influence the narrator/survivor/writer the most will receive the most character development.

This concept takes something that would otherwise seem like story contrivance, and paints it as a logical necessity.

Edit: Consider the concepts of Selection Bias and Survivor's Bias. (Thank you @Vorac .)

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Proof of Peril.
Some characters are killed as various kinds of proof for the audience.
This can be proof of peril for the heroes, or for the innocent.
This can be proof of the ruthlessness of the villain.
This can be proof of the lethal environment. In the opening of Saving Private Ryan many soldiers are gruesomely killed in the war beside Tom Hanks, proving both the extreme lethality of the situation and the stakes for Tom throughout the script.
In Jurassic Park (or many other dino movies), people (and other dinosaurs) must die to prove the dinosaurs present a lethal threat; otherwise simple roaring doesn't feel like enough.
In a "nature is the villain" movie (flood, earthquake, tornadoes, super-virulent disease, asteroids coming), many people must die to prove the threat is no joke, preferably sympathetic characters (e.g. young, elderly, or mother and child, perhaps a family). Similarly for "terrorist attack" and "aliens attack" stories.
This can be proof of our hero's lethality; i.e. Dirty Harry has no problem killing bad guys; Denzel in The Equalizer has no qualms about wading unarmed into a den of half a dozen armed gangsters and killing them all.
If your character is supposed to be the most accomplished warrior on the planet, you need to show him in battle quickly. Brad Pitt as Achilles kills some Goliath champion of an opposing army, in a "scheduled" battle, almost in an instant without taking a scratch.
An early death can be foreshadowing of an important death, e.g. the finale death of a developed character, like the villain, a love interest of the hero or story-long sidekick or friend of the hero.
Similar to foreshadow is personal danger: If the villain in your story kidnaps and rapes cheerleaders, then showing him committing his crime with an cheerleader that looks much like your protagonist not only makes the crime a real peril, it specifically puts your protagonist in the cross hairs, so every time she ventures out alone the audience anticipates peril.
+1 Nicol; there is some economy involved too; if we only need to kill people to prove to the audience there is significant peril, then a sketch of such people is enough. In a movie, their appearance alone can evoke sympathy, or antipathy. We don't need to spend a lot of time on them. A book is more forgiving and we might develop them a little; in a film every second counts, literally. But either way, too much investment delays the purpose and signals the reader the victim-to-be is important, which turns out to be a disappointment when they are killed and have no further impact on the plot.
When we kill somebody to prove something we want the audience frightened or impressed, but it is a mistake to make the audience "invest" too much in them only to be disappointed they just die, and quickly, and this has no more ramifications: Their death is a dead end (double meaning intended).
These characters are props, and like props we limit the audience investment so they feel what we (authors) want them to feel: Fear for the protagonist (or dread or hatred of the villain), we don't want them off on a sidetrack with their thoughts occupied by the interrupted life of the prop, what happened with their venture, or kids, or how her parents and siblings and boyfriend are faring after she is raped and tortured to death. To prevent that off-plot mental wandering, we just don't develop our victims and divulge all that information.
We show or tell the minimum of what is necessary about our "proof of peril" victims, only things that will inform the plot (e.g. the college girl's appearance, the time and place of her kidnapping, that suggest our villain's victim-type and modus operandi).

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Consider the economy of storytelling.

Developing a character takes time. Evolving a character takes time. It requires words in your story to accomplish these things.

That time and those words are units of currency in the storytelling economy. At any particular time, your story is doing some small number of things. During that time, it is not doing other things. Character development is spending currency; spending time on a set of characters is time not spent with another sets of characters.

The idea with writing is that you aren't spending this time currency willy-nilly. You are investing it. And like with any good investment, you are expecting some form of dividend or payoff in the future.

If you unceremoniously kill this character after investing in them, without getting the payoff from that character, then that investment has essentially been wasted. Time spent developing a character whose death serves no or little purpose is time that could have been spent on other things.

Of course, "payoff" can happen in many forms. And there are ways to make terminating a partially-developed character a worthwhile investment in a story. But more often than not, this is a simple mistake. It's just not a sound investment strategy to spend a bunch of words on a character whose character arc is cut off before it can conclude.

This is true for many other aspects of storytelling. The plot of most stories doesn't end before achieving at least some kind of climax. That climax is the payoff for all of the investment in the story up until that point. Simply ending a story 2/3rds of the way through, leaving the plot, characters, and/or themes unresolved, is not a sound investment strategy.

Consider your example, seen through the lens of storytelling economy:

Why aren't multiple characters developed simultaneously, randomly being killed off, with just a random dude from the neighbouring village surviving the carnage?

OK, so you're developing multiple characters. Well, the size of your work does not change, so the more characters you develop, the less currency you can spend on each one. Which means the less investment you have. So killing them off doesn't really lose much individually.

But killing almost all of them off means that in aggregate, you've lost the vast majority of your character investment. And if the person who survives the climactic encounter is "a random dude from the neighbouring village", then that person will have no or minimal investment in them.

Which means that, after spending all of that currency on character development, the storyline payoff is... nothing.

It's not impossible to make such a story work, of course. But you're really marching uphill. In the snow. During a blizzard.

Surprising the reader is not the primary goal of a work. Entertaining the reader usually is. Some readers may find surprise inherently entertaining, but few find it entertaining if you stop in the middle of a sentence.

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Because maintaining suspense over who will live and who will die is only one of a story's many goals. And in most stories, it's not even a very important one.

The fact that The Protagonist Survives is the flip side of the truism that We're Telling The Protagonist's Story. Since what we're telling is the story of one person, or a small group of people, it naturally follows that we need those protagonists alive to carry the story through. (There are, of course, some creative exceptions.) If a writer has a choice between giving a particular character Plot Armor, and having him actually be able to execute the plot, vs. not giving him Plot Armor, and having him die midway, he'll generally prefer a story with less suspense over lots of suspense but no story.

(There are absolutely exceptions. This can absolutely be played with. But as a general guideline, it's much, much easier to not mess around with the concept of "My story has clearly-defined protagonists.")

Other elements here have similar considerations:

Building up a substantial character, only to have him gakked out a few scenes later, would often feel incongruous and unsatisfying. It would be less predictable, yes, but it wouldn't be very satisfying as a story (or, a lot of work would need to be done for such a maneuver to be satisfying).
Conversely, establishing a lowly henchmen who subverts the trope by not dying, would leave him just hanging around uselessly, doing nothing constructive for your story.
Using the device of a memoir or a recounting may be a tradeoff between the possibility of protagonist death, vs. the powerful technique of being able to offer foreshadowing, contrast and juxtaposition, an older and more experienced voice. That tradeoff is frequently worth taking.

There is an exception to all this: Stories where uncertainty and tension are the primary goals. If the story is genuinely trying to evoke a sense of "Who will die next?" or "Nobody is safe!", then yes, they need to be aware of savvy readers, and they can't lean on "important" characters because they can't grant
"important" characters any safety.

These stories are rarer than you might think. Even horror stories generally have a protagonist or two; you want to see them survive and succeed, more than you want the real possibility that maybe they will die in the second act. Action-adventure stories and thrillers may make much of the risk to life and limb, but generally, the audience is there to see how the heroes win, how they inch back even from bleakest catastrophe, more than they actually want authenticity in the hero's chance of being killed. (Even something like GRRM's Song of Ice and Fire can be described more as offering some fake-outs as to its protagonists are, than as not having protagonists.)

But they do exist, and they need to use a lot of tricks, like multiple protagonists (so some kind die), or a non-protagonist viewpoint (so no one character is protected); or maybe they concern themselves with setting or social systems or some other focus that doesn't require a particular cast of characters to survive from start to finish.

This kind of story is fairly rare, and takes a lot of thought. Perhaps comparable to a mystery story, where it's crucial to keep up a fair amount of suspicion on almost everyone for the length of a story. And even there, savvy readers start looking out for whatever character is least suspicious, or played by a well-known actor... Mystery stories, indeed, are entirely focused on the question of who is the murder; much like a hypothetical story entirely focused on the question of who will die next. They exist, but most stories aren't really about that.

TL;DR: Yes, a lot of things in a story work against tension of whether important characters die. That's because most stories have a whole lot of things going on besides that one specific tension. It's a tradeoff that's often worth making, because it serves the story's most crucial goals.

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