Yes
Nah. Can't go there. Think of all the classic stuff we'd lose: The Time Machine, the entire Terminator franchise, much of Planet of the Apes, Twelve Monkeys, Time After Time, Somewhere in Time, Back to the Future, Groundhog Day. And, oh yeah, Doctor Who.
Heck, in Trek alone, we'd lose City on the Edge of Forever, Tomorrow is Yesterday, Assignment: Earth, All Our Yesterdays, The Voyage Home, Yesterday's Enterprise, Tapestry, Star Trek: First Contact, Trials and Tribble-lations, Little Green Men, Future's End . . ..
It may not always be consistent, but time-travel has given us plenty of great stories. And it's got a pretty good track record where Trek is concerned.