Having played Achron I have visited the thought space a lot before.
The thing that allows for time travel might break a lot of your other presumptions. If the moon was made of cheese were would all the milk would have come from?
I would like to point out that the assumtion that timelines are stable is a separate assumption from time travel. I think it needs argument and argument from lack of imagination is not a very convincing one.
However even if you go outside of this assumtion were similar things still happen. In another attempt one could argue that if a grandafther paradox has 2 viable states then both of those states should sum in probablity to a state that is “stable”. So you assign less probability to things that can grandfather paradox. If a thing can attempt to paradox in multiple ways you have keep splitting the “measure”. The end result is that a thing that can constantly paradox will be vanishingly unlikely to hang around. This is different than “mysteriously prevented” but for these purposes serves a similar function.
After all if quantum superpositions are not prevented why would “timeline superpositions” be incompatible?
It is noteworthy that invention of timetravel technology is an event that probably has causes. Anything that utilises such technology would be causally dependent on that event. But that even is causally dependent on other events. Thus it might be counterproductive to have any timetravel technology effect any cause of time travel technology. This would effectively mean that all of pre-timetravel history would be “natural reserve” on the pain of death of all timetravel history.
The is a reverse effect where is a time machine can help with its construction it might be tempted to do so provided it doesn’t undo it more than do it. Even the slightest chance of a working time travel method would be blown to optimally early time travel (within the constraints).
That is fiction has plenty of timetravel reasoning to throw around. Specifying your poison would go for a long way. For example rpg game continuum has slipshanking. Having a sudden fight? Grab a pistol from nearest container. Then after fight go to a shop buy gun, go to past and put gun into said container. Timeline is stable, but it feels weird taht realising that you could try do somethign makes it possibel for you to do so (this kind of reasoning has limitations, if you have openend the box and seen it empty you obviosly can’t slipshank a pistol out of it. But being strategically ignorant in order to maximise slipshanking possiblities is interesting). The ultimate slipshank would be to do it before time travel is invented with the intention to invent time travel to pull it off