All they do most of the time is force the student to add pointless fluff to their essay. If you can convey your meaning in 200 words, but the requirement for the essay is 300 words, then most of the time they will just reword things to make them longer- change 'didn't' to 'did not', change 'like I said' to 'as noted in my previous paragraph', and slowly dilute the point they are trying to make with more and more words, until the point is only 1/4 of the essay, and the other 3/4 is filler to make up for the teacher's requirements. Yeah, maybe sometimes you'll get a student to elaborate, or add another viewpoint, but if the student thinks that the essay is done, then they wont add anything important, and you are just forcing them to sabotage their essay. If you can clearly make your point in 200 words, there is no reason to say it in 300. Say you were tasked to describe a ball. You'd probably say something along the lines of "A ball is a circular toy.". But if you have to describe it in a minimum of 100 words, then it would start looking like "A ball is a common three dimensional spherical toy. They can be almost any size. Balls can be bouncy or hard. It has gained popularity as a toy because of its many different ways of playing with it. Most sports use balls. They can be as small as a marble, or as large as a yoga ball. Blah blah blah etc etc" And soon you start going off on tangents and lose the point of the essay.
You might have noticed that the title sounds a bit weird- thats because I was proving my point. I was going to title it "Why Minimum Words Count Shouldn't be a Thing" but by making it longer to "Why I Think That Minimum Word Count Requirements and Minimum Page Counts Should Not Be Necessary in Essays and Assignments,". I haven't added anything important to it, only made it more laborious to read. I said the same thing in 8 words as I did in 18 words, and nothing was gained from it besides sounding more forcefully scientific.