Yeah, putting that way your side of the story does sound more reasonable, but i feel either choice for jack makes a good degree of sense (while still having some sort of heavy sacrifice to it).
Again, its at least nice how we sort of got both possible sides for an ending via the comics (jack stays and builds a better future) and the final season (jack goes back, avenging his family and saving the future from aku).>It was so easy to pull a "Foolish Samurai, even if you defeat me in the past the future that is I, Aku, will still exist" since we have a fucking primeval being made of pure evil that can make time portals, having a "both timelines will still exist because timey wobly magicky aku stuff"
Not really, in the series at least Jack managed to kill aku for good (even if the fight was really anticlimatic), as the sword was the only weapon that could TRULY end him, thus saving the future from being fucked over by Aku.
The whole point of Aku being unable to just swoop over and murder jack throughout the series, aside from jack being very skilled, was that he had the only thing that could kill him for good, unlike the previous methods used to stop him.
Aku having the hability to go to different timelines is a whole different deal, hard to say when that side of his powers aren't really explained.