I've often mentioned that we have a wonderful community, and these stats help support my sentiment.
One of the stats that makes me the happiest is that, as moderators, we literally did not have a need to suspend a single user. On top of that, our community did not need to suspend any of the moderators! :)
Such answers should be allowed and if there is an explanation why it's impossible such answer can be really useful.
So, some example for a question with an "it's not possible" answer could be: Which software calculates (not brute force) the private key from a public key for some really powerful encryption.
I think that we should we allow "It's impossible" answers for the following reasons:
Such answers are useful to inform the OP and other readers of the difficulty or impossibility to provide a program that satisfies their requirements. Amongst other things, this may allow the OP to refine their requirements to make it more possible. Other answers ...
I don't want such answers. They don't help me. And thus I downvote, because that's exactly what the downvote means: "it is not useful".
When I ask a question, I have a problem and I want to solve it. Someone telling me "it's impossible" is much like a "killer phrase". I've had that often enough in the companies I worked for. And ...