Of course, this has its own moral dilemmas as well—such as the fact that you’re as good as dead for your loved ones in the timeline that you just left—but generally smaller than erasing a universe entirely.
You could get around this by forking the time traveler with the universe: in the source universe it would simply appear that the attempted time travel didn’t work.
That would create a new problem, though: you’d never see anyone leave a timeline but every attempt would result in the creation of a new one with a copy of the traveler added at the destination time. A persistent traveler could generate any number of timelines differing only by the number of failed time travel attempts made before the succesful one.
You could get around this by forking the time traveler with the universe: in the source universe it would simply appear that the attempted time travel didn’t work.
That would create a new problem, though: you’d never see anyone leave a timeline but every attempt would result in the creation of a new one with a copy of the traveler added at the destination time. A persistent traveler could generate any number of timelines differing only by the number of failed time travel attempts made before the succesful one.