This idea has come up many, many times before. If you're focused on questions that shouldn't be closed, it's a very appealing notion: it makes it harder to close them.
Of course, it makes it harder to close questions that should be closed too, since even a minority of contrarian voters can increase the number of close-votes needed to close anything. And the truth is, it already takes a lot of work to close most questions.
...which, of course, is the intent. Originally, it was really easy to close questions. If you had the "close" privilege, you just clicked close and... it was closed. No muss, no fuss. Well, except that there was no need for any consensus on why anything should be closed and if you wanted to be an ass about it the system just went ahead and let you. So things got a bit harder and then a bit harder still, and realistically it's now slightly too hard in some scenarios and slightly too easy in others, but for the most part it seems to work (there's another suggestion floating around to scale the number of votes according to active users on a site that might help a bit, but in practice it's usually easier to get a moderator to handle the edge cases).
Point being, it's easy to make it harder to close things: increase the number of votes required, tie that number to the post's score, or views, or age, or whatever. Heck, if we're just concerned about popular questions getting closed, disallow closing anything with a score > 0.
But popularity doesn't necessarily equate to quality or usefulness or connection to the topic of the site. That's why closing (and re-opening) has always been separate from voting, limited to fewer participants with a larger stake in the site and stripped of the normal rules of anonymity that protect normal voters from scrutiny. Turn it into a parallel popularity contest and you might as well just not bother.
Oh, one last thing:
This way border-line questions don't get closed too quickly, if at all.
I believe it's generally more harmful for questions to be closed slowly than quickly. If someone makes a mistake, tell them right away - that way, they can learn from it and do better the next time around. Telling them days or months later doesn't help. Worse yet, if the question collects answers in this time then you're punishing them too. The biggest down-side of the view-based vote aging rule is that it can keep votes hanging around for years; at some point, this starts to just get silly. The close review queue changes should help with this eventually, but we have a rather large backlog to go through first.