I looked through some of the closed questions, expecting to see spam or youtube-level drivel, but I didn't see a single case of that. What I found was perfectly serious questions related to math. They were often interesting and/or valid mathematical or math-related questions (as judged by the number of answers and high-rep level of answerers).
The FAQ says that questions get closed for being off-topic. It also gives examples of what sorts of questions are considered off-topic. Basically your question needs to be in a non-math area (physics, engineering, financial, latex, numerology, meta) to be off-topic, according to the FAQ. In practice, very few of the closed questions are off-topic by this definition.
An interesting case is what looks like a crank question about 1+1=3 which received 4 answers, all trying to be helpful, all different. It turns out that the asker was perfectly serious, and they accepted the answer of the type they were seeking. Isn't this the system working exactly as desired?
Another case asks about $(a+b)^n>a^n+b^n$, a legitimate question with 6 legitimate answers, closed as "too localized" in part because it "has been answered quite completely". Huh? I am completely missing the logic as to why that was closed.
Closed questions can be found in searches, so the only effect of closing seems to be (1) prohibiting further answers, and (2) giving negative feedback to the asker and any answerers. It is hard to see the utility of (1) (nobody is obligated to answer any question anyway — if somebody wants to answer, why should they be prohibited?), and it is also hard to see the utility of (2) (if people are asking and answering, why not let them? anyway, use downvotes for negative feedback).
There is one more effect, namely that in the long run, closing questions of certain types has an effect on the overall focus of the site. High-rep people can in this way steer the site as they like. In fact, any quorum of 5 can steer it, which is less than 10% of those eligible to vote!
If one thing is clear from both this question and the recent "deleted Pete Clark comments" fiasco, it is that different people have different visions of how this site should operate. This is not surprising. In fact it is unavoidable. What should be obvious is that the site is big enough to accommodate us all (tags exist to help each of us focus on the parts we like). And the other thing that is clear from both this question and the recent dPCcf is that when you start censoring (instead of just ignoring) things that other people don't think should be censored, people will get upset enough to consider leaving the community.
So those with the power to close have a choice: Use closing to try to steer the content, generating enough bad vibes to lose top contributors every so often, or keep the closing to what everybody can agree on, even when you yourself would close more.