I have no problem with most worlds ending in tragedy, as you say it makes it more meaningful. The real reason I'm pushing this view so much is because this is an opportunity to test that view against someone who knows the story well.
The transfer of memories was useful, but I don't see the point of saving one world when she knows so many others are out there that are fucked anyway. Other than for the benefit of saving her own life of course. That's just me though I suppose.
The idea that they are all completely separate worlds makes the whole fate concept very iffy and ignores how the other characters can vaguely remember previous worlds. However, viewing them purely as resets also causes issues, which you have pointed out.
I think a better way of looking at it is a combination of the two; that each new world is a reset of a sort, but that the original world also persists. So she's not really travelling to completely separate worlds, but rather creating/entering modifications of the original - subworlds if you will.
This would explain why the other characters start to accumulate memories from the other versions, and why the fate of the original world affects the other worlds - because they are all tied together. But this also views them as separate worlds in as much as the original versions still exist even after she 'resets'.
So its a combination of both, which I think is consistent with everything.