The rationale behind closing questions as "too broad" is that:

There are either too many possible answers, or good answers would be too long for this format. Please add details to narrow the answer set or to isolate an issue that can be answered in a few paragraphs.

What if we adopt a more specific solution to this problem instead of closing the question?

Just as SE sites display only the first several and most upvoted comments under a question or answer, we could display the first most upvoted answers if indeed there are too many answers to questions deemed broad (the rest of the answers would be hidden underneath a "Show more" heading - Quora does this and it works very well). It also may be the case that question won't actually generate too many answers, which suggests that the decision to close might have been suboptimal.

In both cases, everyone wins: the asker gets to have their question answered, answerers can contribute, nobody feels censored, and the site stays clean.

I believe there is already some UI in place for greying out answers with many upvotes?

UPDATE: at 10+ downvotes and no answers, I'd be curious to learn what the counter-arguments for this proposal are.