I think Timetravel can work in a story. Really its just taking the prophecy shit that is in every other fiction story to its logical solution. I actually have an idea based all around time travel and how the different types of timetravel would interact.
Then again I was lead to the idea when i was thinking up ways to come up with the most complicated, convoluted story ever so...
Paradoxes, Timeloops, Parallel Universes, etc.
They certainly don't have a place in every story, but the ones they do are usually interesting for some reason or another. I feel like just dismissing it outright is closing off an avenue of exploration in a certain type of story.