I agree with Andrew Leach's answer (close off-topic questions regardless of answers). This answer expands on his closing paragraph.
SE is about building an archive of expertly answered questions. There are three broad status levels: open, closed, and deleted. Between 3K and 10K rep, we can move questions between the first two.
Closing a question simply marks it as being of questionable relevance to the site. From the perspective of SE as an archive, however, this has little to no effect on search. Anyone can still view closed questions and their answers.
What closing does is feed into the deletion process, where higher rep users can take the question out of the repository altogether as far as generic searches are concerned.
I think your question is primary about the point of closing questions when it doesn't prevent the asker from getting an answer:
Considering at this point the OP basically got what they wanted even though it should have been closed rather than answered, is there really any point in voting to close it?
The fact is that we are a very diverse community. People find interest in all sorts of things that others don't. So people will answer questions that others find completely uninteresting. This may help the OP, or it may not. I don't think it's necessary to police this - if the question is so bad that it gets deleted, the answers and comments will also disappear. If the OP is helped in the process, that's between the answerer and the OP. It shouldn't factor into the decision to close or delete a question on grounds of relevance to ELU.
I suggest that the primary factor in reviewing questions for closure should be whether it is a good fit for ELU - that is, whether it is something that etymologists, linguists or English enthusiasts are likely to find interesting.