I feel your pain! I help with hiring college student interns for my office--as in, all the emails come to me--and even though we have barely any
requirements, I frequently get emails from people who manage to miss the minimum. Like, they aren't students at our college! Or I say in the ad, "Must be able to work summer," and they say, "Oh, but I won't be able to work in the summer, is that okay?"
No, it isn't! But, you know, they're hustling, they figure it doesn't hurt to ask or try anyway, and they don't think about all the other people who are doing the same thing.
My policy is to always respond, because like you I know how disheartening it can be to get no response at all. If it's a very clear NO--like the people who can't work summer--I respond to tell them no thanks, we're only looking for people who can work in the summer. (I copy and paste my sentence from a document, makes it much easier.) If it was something where you had to evaluate their resume a bit more, and you personally didn't think they were qualified but it seemed like there might be some wiggle room, I would just say, thanks for applying, but we're going with other candidates, or the position has been filled, or whatever. In other words, I think saying, "You're not qualified for this job," would just lead to arguments from some people, and that's unpleasant. I'm sure they know
they're not qualified, they're just hoping you're flexible on that requirement, and it's not really your job to help them understand, you know? You can just say no thanks and move on.