This is how I use Stack Overflow: I search for a question on Google, and if a Stack Overflow result shows up, I click on it and view the question and answers, and up-vote if I find the information useful. Using it this way, it does not matter if there are hundreds of questions that are "too broad" or "not a good fit for the Q/A format" or "not likely to be useful to others". I simply don't see those, unless they are relevant to what I am searching for.

So, is it not better to have lots of questions of which any of them will only show up when people are searching for them? Or is it better to close questions that people might actually be searching for, in order to have a "cleaner" overall set of questions?

To me, it does not seem to matter if there are lots of junk questions on the site, if no one will actually see them!

My personal opinion is that there are plenty of questions that get mob-voted closed (I guess that's fun for some people maybe?), that really could be helpful for a subset of people out there. If the rest of us don't see it, what's the problem?

I think legitimate reasons to close questions are 1) they are duplicate or 2) they are very poor quality where it really would not be very comprehensible to someone searching for it.