I don’t know whether to be gratified that Oak got to the heart of the matter, or disappointed that it took him so long.
The only concern is how history preserves itself. If history says Manhattan doesn’t get nuked and you’re trying to nuke it, then the simplest way for history to be preserved is for you to be deleted at the point where you try to do something too big to be ignored.
You can’t nuke Manhattan in the 1943 for the same reason Adolf Hitler can’t nuke Manhattan in 1943–1943 already happened, and Manhattan wasn’t nuked. In this scenario there’s only one time line, and everything that happens has already happened. This implies that there won’t be very much time travel into the past, because if there was we’d already know about it.
The even simpler way for the space-time continuum to protect itself against meddling time-travellers is to prevent the invention of time travel. If there’s some sort of cosmic censorship principle in action, that is. Hard to distinguish this sort of universe from the universe where alteration of the past is possible, and happened a lot, until all the time meddling resulted in a universe where time travel just happened to never be invented.
The paradox of “when was time travel invented?” is a pretty tough one. After all, if you invent a time machine and go into the past, then the time machine exists in the past. Why not travel back to ancient Egypt and teach them to build time machines? Or the Carboniferious Era? I know if I had a time machine, the first thing I’d do is travel back in time and give my past self the plans for the time machine, so I could build a time machine and go back in time and give myself the plans for it. The fact that I haven’t been given a time machine by a future version of myself is evidence that I will never have a time machine.