Since "write an essay" can be anything from three paragraphs to a 50 page paper and the teacher probably doesn't think either is the appropriate response to the task, some sort of numerical guide is a good starting point, even if a fairly wide range is a better guide than just a minimum...
(plus actually there are real world work tasks involving composing text that fits within a certain word range, and since being concise and focused isn't AI text generation's strong suit, I'm not sure those work tasks will disappear...)
My high school professors had a really good solution to this:
Minimum word lengths but you have to write the essay in class by hand. You have 2 periods.
Some of us still write a lot but having limited time and space (4 pages) really put a hard limit without saying so. In higher classes they started saying “I’m gonna stop reading after 3 pages so make sure you get to the point”
Demanding that students mind read is not a good strategy. Specifying expected length, checking for it is a good strategy. Teacher should also check for other things - whether paragraphs logically follow, grammar, sentence structure, you name it. But dont make them guess.
Subject yourself to a classroom of kids that you must teach to write, and throw out minimums. Will some students do fine? Sure, of course, and what of the others that turn in one sentence? That never grow? That have to go into the math class and hear their idiot parents say "why are you learning that we have calculators"
Strawman argument; the correct thing to do is not to throw out minimum word count and leave it at that, rather to emphasize the role of brevity and concision while still being sufficiently thorough.
It's widely understood that LOC is a poor measure for many coding purposes, so it shouldn't be controversial that word count is an equally flawed measure for prose.
While I hated it in high school, but think I better understand it now. I think part of the problem is they never explained the "why" or the "how", just the requirement. I wasn't able to write anything more than a page or two without extreme difficultly until college when the requirements went up to 30 pages.
In theory, someone who can write a 30 page paper could effectively distill it down to a short memo when needed, summarizing their primary point(s). Someone who can only write short memos would have a hard time writing something longer one day if/when required. I was trying to do a knowledge transfer one day, opened up Word, and just typed 20 pages on everything I knew about a tool we used heavily, but wasn't documented anywhere. I don't think I could have done that before I was forced to write those longer papers in college.
John Nash's Ph.D. Thesis is notorious for being short: it's still 27 pages (typed, with hand-written equations and a whopping total of two citations) but that's an order of magnitude below average. On the other hand, most of us don't invent game theory.
Students used to minimum-word-count essays sometimes have to do some self-retraining to realize that the expectation is that you have more that you want to say than you have room to say it, and the game is now to figure out how to say more in fewer words.
Same as lines of code, etc.
I certainly wish more teachers encouraged parsimony and penalized fluff and bullshittery, but I'd be surprised to find them doing it outside of some narrow cases where the point is just to make you write something at all.
Tthey generally want to encourage their students to engage with the topic at a certain level and practice the thinking needed to research, structure, and implement an argument of a certain length. They want you to put at least 5 pounds of idea in the 5-10 pound idea bag.
If you're convinced you've hacked word economy and satisfied the assignment except for this goshdarnpeskyminimumwordcount, you're probably misunderstanding the lesson the instructor is willing to read through a bunch of bad writing to impart and cheating yourself.