^Well, I was stuck with the premise that a timeline can "replace" another one, since Trek has used that plot device so often. So I had to find a way to reconcile it with the common-sense reality that alternate timelines would coexist. What I came up with, as explained in the book, was the idea that the original and altered timelines do
coexist -- until
the point in time when the original time travel occurred. For instance, go back in time from 2267 to 1930 and save Edith Keeler, then the Nazi-Earth timeline runs alongside the standard Federation timeline until the moment McCoy jumps through the Guardian in 2267 -- and then the two parallel timelines converge, with the Naziverse replacing the Primeverse. That is, only the Primeverse exists prior to 1930, then Primeverse and Naziverse coexist from 1930 to 2267, then only Naziverse endures from 2267 forward. Which is why the landing party saw the universe change around them right after
McCoy jumped back -- they literally witnessed one timeline overwriting the other at that moment and not before. (Although it didn't really, since Kirk and Spock going back and restoring their original history is part of the whole mess too, so it's more like the original history was only temporarily suppressed and then restored.) It had
still happened, nothing can undo that, but after a certain point, if Kirk & Spock hadn't undone the change, then nobody would've remembered anything from that version of history, so it would seem to them as if had never existed.
The thing is, quantum physics does theoretically allow for two divergent timelines to reconverge; it's just very, very unlikely, and since it entails reducing entropy, it would require some kind of immense exertion of energy/work to make it happen. And if it did happen, then quantum information theory demands that only one of the two conflicting versions of events could survive. So it's not complete nonsense that it could happen this way. It's theoretically possible, just extraordinarily improbable. I had to concoct some imaginary physics as a fudge factor to justify it happening in the Trek universe.
But still, that means that the natural, default outcome should be that the parallel timelines coexist indefinitely. If it takes a special set of physical circumstances to cause the altered timeline to reconverge with and overwhelm the original, then it stands to reason that if those circumstances aren't met, the two timelines can and will continue to coexist. So while the effective erasure of a timeline is a danger that can
result from time travel in certain cases, there are going to be other cases where it isn't a risk. Which is why we see instances like "Assignment: Earth" or The Voyage Home
where the time travel seems to have no effect at all on the timeline, or instances like the Abramsverse and implicitly "Yesteryear" where it creates a stable parallel.