: When is it acceptable to refer to an undefined group of people in academic writing? Within my students' college writing, I found much writing referring to essentially imaginary, or not well-defined

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Since your question is specific to academic writing, I would encourage you to continue to push the students to develop clarity and specificity in their writing. We expect academic writing to be rigorous in terms of backing up claims that are made. Allowing your students to get away with the kind of vague and generalized claims you provided in your examples is not doing them a favor for their future career, whether in academia or industry.

Related to that, I would add that merely being specific isn't enough; you need to back up your claim with references (unless, of course, they are writing fiction! In which case the rules can be what you as the instructor make them, although I'd still encourage students to be precise and concise).

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I think the problem is not the broadness or the ambiguity in the identification of the group, but rather whether there is any evidence to back up the claim.

A statement like, "People have an average body temperature of 98.6 degrees" could be completely accurate even though it's very broad. A statement like, "Hispanics who live in Boston all like pineapples" is surely false despite being pretty specific.

That said, vague identification of a subject group can be a sign of weak thinking or even deliberate deception. I often hear people say things like, "The American people want the president to do X". At best this means "polls show that a majority want". Often I think what it means is "my friends and I want". I think lots of people fall into the trap of observing, "All the people that I hang out with at such-and-such a place agree that ..." and leap from there to "People agree that ..." Sometimes this should be obviously ridiculous, like just because all your friends at the National Coal Miners Association agree that coal is the energy source of the future surely tells us little about what the folks at the Green Energy Coalition think.

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When is it acceptable to refer to an undefined group of people in academic writing? I'd say only when such group has been defined previously in the text.

Academic writing is about specificity. Think of dictionary definitions. What makes a definition valid? That it can only be applied to that particular thing you are referring to (you wouldn't define a rat as a 4-legged creature, because a cat is also a 4-legged creature).
In the same 'spirit', I wouldn't define something I'm describing with generic terms, unless I have defined it before, usually in the introduction. Perhaps that would be a useful reasoning to tell your students.

"In this essay I will analyse the incidence of increasing gas prices
on German IT technicians carpooling to work (...) Carpoolers changed their behavior after the second rise in prices..."

I see "These days, more and more people carpool to work" as a valid statement in a magazine / newspaper article. As mentioned in this answer, for academic writing, it's too vague. What people? When? Even if the statement has an attached note (Person, 1984), 'more an more people' or 'some people' are still not good subjects. In my opinion, they need to be defined more specifically, so the statements that contain them can stand by themselves.

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I don't see that "more and more Germans" is much better than "more and more people." Both are vague. How much more? 1% more? 90% more? And compared to when? yesterday? last century?

In the introductions of journal articles, you will often see statements like "recently, there has been interest in blahblahblah" but such vague statements are backed up by references to several previously-published journal articles on blahblahblah. The references quantify "recently" and "interest."

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