My point of view will be no surprise, but I'll put it here so that we can vote on it.
If the question doesn't ask for opinion-based answers, it should not be closed. The answers should be dealt with, and the question could be clarified.
If the question has no bad answers yet, and the OP may be helped by answers that do follow our guidelines concerning references and so on: edit the question to make it a reference-request and check with the user if that's okay in the comments.
If the question already has bad answers, and the OP doesn't particularly seem to like them: remove the answers or invite their writers to improve them (perhaps put the citation-needed notice on it) , and edit the question to be a reference-request
If the question already has bad answers and the OP likes them, in the way you described above, close the question.
I do not think such new policy should be applied to old, frequently visited questions. Instead, they could be locked, like is done on Stack Overflow.
We will need a page to refer users to when they don't understand that their post doesn't fit here considering our ideas of references and so on. I don't know of a help center page that explains this very well, or a much upvoted post here on meta. Otherwise, we have to discuss about this with every new user again...
Anyway, like this, I think we lose as few questions as possible, and we maintain quality.