This definitely wouldn't work in pure math, as there's nothing so "destructive" you could prove that wouldn't make you a celebrity among mathematicians. Finding a contradiction in ZFC would get you a Fields medal. Disproving the Riemann hypothesis would get you a Fields medal *and* a million dollars. There would never be any question about *whether* to publish, only how quickly to do so.

Now, if one wants to get a little silly, a world where P = NP and NP has efficient algorithms is one very unfriendly to mathematicians. In such a world, proof finding (that thing mathematicians pride themselves on) is no more difficult than proof verifying (that thing that mathematicians spent a lot of effort to get machines to do for them), so they'd mostly be either out of jobs or monitoring the automatic proof-finding machines. Perhaps this would be a reason mathematicians wouldn't want to publish such a result, as making your entire job redundant is widely considered a bad career move. Though, since that result also solves a huge number of practical problems, breaks all public-key cryptography wide open, and wins you a million dollars, I can't imagine it staying secret for long.