By observing many questions which are still left out there I'm starting to get an impression that this community never bothered to close questions although when they were worth closing.
There is post which explains "Why is voting important?" and "When to close", but there is nothing which explains "Why is closing important?"
From here we get something like "It's all about signal to noise ratio". But why?
Well in Stack overflow, it was to save the time of answerer. But I don't know what could drive a person to take the initiative to close questions here.
But all I can do is point to some thing which is already there
- Close boring, trivial, mindless, uninteresting, etc. questions.
It's taken me a long time to get here, but I'm convinced that you really need to shut down any question that wastes your top-users time and energy. Flag these questions. Vote to close when you get the privilege. Comment. Vote down as appropriate. Don't forget that you can always edit and reopen a question, but you can't refund the time and energy users spend answering unfocused questions or arguing about unsupported answers.
as seen in here https://islam.meta.stackexchange.com/a/284/11938
Here's a piece of advice.
In case if you've missed this part i.e. when do you get the privilege to close questions, answer is 500 rep, but even before that users less than 500 rep can still take the initiative to close questions by simply flagging and by letting the mod close questions.
But overall, I don't know why should I care to close questions here in this site.
Update: For users access to review queues, they don't seem to pretty much actively participate. Even if the question is worth closing, the questions get the close votes very slowly like it takes 2 or 3 days or even weeks for 5 votes to accumulate.