I have (semi-*)seriously considered the possibility that time travel would in fact instantly destroy the universe (not the multiverse though). One of the theories on what happens when you time travel is based on “postselection”, see also youtube video by Seth Lloyd: what you get at the end is what you’d expect if you just discarded any final state that led to a contradiction with what you put in.
Now Seth Lloyd says you then renormalize the probabilities. But this renormalization seems an extraneous assumption to me: a more natural interpretation to me is that the amplitude that would otherwise be associated with the contradictory possibilities simply disappears. It would be hard to time travel without having to have a camel-through-the-eye-of-a-needle level of contortion to prevent some contradiction, so time travel would in effect reliably destroy the universe if it were ever used.
*I am bad at taking things seriously, or I probably wouldn’t post this—e.g. imagine if our lack of time travel is due to the anthropic principle. edit: we should have a greater expectation on hypotheses that have more observers in our situation, so we should expect that, conditional on time travel being deadly, it’s probably too hard for us so far and not merely that the worlds where it has been invented are gone. Whew, that’s a relief (for now)! If anyone reading this does discover an easy time travel method though, DO NOT USE IT.