AV.SE, and SE in general, exists primarily to answer difficult questions, ones that haven't been answered in your basic textbook. Or, if they have, to answer specialist-grade questions in a way that a layman can understand. Or to give a broad perspective on open-ended, controversial, or simply interesting questions.
Most homework questions are none of that.
The answers to them are well-known, unambiguous, and rarely of interest to a wide audience. The people asking them aren't looking for perspectives or insight, but to circle the right letter or skip a lengthy calculation.
Some exceptions are bound to exist somewhere, but they would be the exceptions that prove the rule! The few homework questions that are genuinely interesting often won't be identified as a homework question, and will receive all the attention such a question normally would. If they're clearly revealed as homework, that can be fixed by editing out the homework bit.
It's when a question is so uninspired and uninteresting, that it's hard to think of any reason anyone would ask it, other than homework, that it gets and should get close votes for that.
Downvoting is not a replacement for closing. Downvoting works well on answers, as a way for the community to mark wrong answers. For questions, downvoting is much less effective at removing their effects on the site, not to mention the negative externalities.
Bad questions actively harm the site. They are useless for everyone except for the asker (or someone else with the same piece of homework). They still show up in search results, so people trying to find knowledge on the site will find A, B, C or D instead.
Such questions are noise that reduces the site's usability and quality. These are decisive today - there's no shortage of information on the internet, the challenge is sorting the good from the bad, getting the best signal to noise ratio.
In conclusion: We should close such questions, but without prejudice.
Open-ended, on-topic questions that invite interesting answers should stay regardless of their origin (and edited to abstract them from homework if needed). Questions that have no value aside from cheating on a test should be removed.
Heavy downvoting can hide them, but that is worse for the user than a swift closure with explanation on how to ask a proper question. We're closing questions, not users - the best outcome is for them to identify their gap in knowledge and ask a better question that helps them understand the topic they're studying.
Recently there's been a practical case in question: How many smoke detectors does the A340 cargo deck have, and how are they wired?
This is what I feel is an example of a decent homework question. The question is not the actual assignment, it's knowledge to be used as an input for one. In such cases, it's probably not even necessary to remove the homework context - as the student's faculty member, I'd be inclined to answer it or at least suggest a book.