Some things can be fixed, but undoing something is another matter altogether. And the whole thing comes to mind, because it comes up in songs with fair frequency. "Even knowing the unhappy ending to my story, I would have done it anyway, because it was worth it," says the narrator in one poetic form or another. If you'd like a concrete example, take Michael Longcor's very fine Pegasus-winning song, Shooting Star.
And I just can't accept that. I can easily imagine that there are circumstances where it is absolutely necessary to sacrifice your life for something, but I can't imagine that you'd do that if you knew enough about the situation in advance to avoid the whole set of circumstances in the first place. If you knew that the shuttle's external tank was going to drop a chunk of icy foam onto the thermal tiles and shatter them, you wouldn't say, "Well, there are risks and it's all been worthwhile, shame that I'm going to die now." You would figure out how to fix the damned problem -- given sufficient warning, of course.
I think that this is part of the attraction of Bill Murray's Groundhog Day. The hero gets to try to solve his problem over and over and over again, until he finally gets it right. (Some problems, such as the dying bum, remain insoluble in the course of a single day. Not enough warning to get it fixed.)
I don't know if this need to fix things is just a guy thing (as my wife, daisy_knotwise, has suggested) or if it's just a me thing. There are so many things in this world that could have been fixed by a little bit of foreknowledge -- assuming, for the moment, that any attempt to use such foreknowledge isn't automatically doomed to fail, because that's just depressing. (Even for me!) The fact that these things have still happened suggests that time travel into the past is one of those "not-allowed" features of the universe we're living in.
Either that, or our time travelers shot their wad preventing the nuclear exchange between the U.S. and the U.S.S.R. back around the time of the Cuban Missile Crisis. After all, that never happened, right?
Or maybe someone just finally figured out how to fix it.