Depends on the method of time travel, and how the universe works.
If we live in a universe where time travel can only be used to observe, or the universe itself prevents changes from being made via stable time loops and ridiculous coincidences? Then it would be mostly fine (though it might become like a higher level of doxxing, where you could go back in time and see what people were doing years ago, potentially film blackmail material, or otherwise find ways to see and learn shit you really shouldn't be).
On the other hand, if time travel CAN alter the past, and doesn't involve multiple parallel timelines and infinite possibility shenanigans, then time travel would be the most dangerous thing ever, even if it wasn't public. The moment anyone (theoretically) can time travel, even aside from the various "I'm going to back and fix the past!" factions starting time wars, you'd have people like me going back to try and find a way to keep humans from evolving in the first place. Or deliberately creating Grandfather Paradoxes in an attempt to self-destruct the entire universe.