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I think minimum page requirements are a good thing because they (i) force you to develop your ideas further than what you might be comfortable with and (ii) they give you a guideline to the depth of coverage that is expected. You usually approach a four-page paper differently than a ten-page paper, or at least that's what I do.
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I think this is totally right. I have a parent who is a prof, and they've explained min and max page #s in terms of trying to give students a sense of the depth of coverage they want, especially. Basically, my parent said "Yes, sometimes a student is two pages under because they are REALLY concise, and it is still a great paper. Sometimes they are two pages over because that is their style/their argument was interestingly complex, and it is still a great paper. But normally, if a student is really off of the page limit, they are either not making a deep enough argument, or they are trying to cover way too much, and it is not so good a paper."
Basically, it's good to learn how to tell exactly what your prof is getting at with the limits. For example, some people I know think its good to go way over the page limit b/c the prof will be impressed or something, but most of the time that means they are approaching the topic too broadly. Many profs see value in being able to narrow your argument so as to not go over the limit as much as being able to make it broad enough to hit the limit.