Minimum word lengths were really a terrible idea and I wonder what arguments were used to get all the teachers to buy into that system.
Have a second of critical thinking on this topic will make it abundantly obvious why this line of questioning is anti-education and anti-intellectual. You write in school to practice. No just composition, but grammar, spelling, individual sentences. Practice requires volume.
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"
It can help to force depth into a topic that requires it, and more expression and emotion into writing where that is of value. It also forces the writer to think more deeply about the topic and organize their thoughts.
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.
Where I encounter it at the higher education level is that academic-level research almost universally has maximum word counts or page counts rather than minimums: if you think you can get your point across in fewer words, you should. No reviewer is going to object to the paper being too short, so long as you succeeded in making your case.
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.
Journalists and writers are often given a deadline and a target length. "Give me 500 words of copy by the end of tomorrow." The editor and publisher of a magazine need to get all words and graphics ready by a strict and regular deadline.
It’s easier to judge an objective output like number of words than subjective like quality.
Same as lines of code, etc.
The idea was to get people to include more substance. Instead of just saying "Washington crossed the Delaware" to get students to include reasons why, impacts, further narrative, etc. IDK if it was effective or not. Probably at least a little; there's only so many ways to rewrite the same thing over and over. I know in my case though I submitted essays below the word count a few times, but since I actually included the content they were looking for I didn't have any problems
Considering that many high school kids won’t want to put in any effort at all, how else do you convey the amount of detail and effort you expect for a given writing assignment? It’s an imperfect proxy but I can’t think of a better one.