To be fair, do we even know what rules time travel in our universe would work under? If someone changed the timeline, would we ever even notice? Or would the world just change abruptly in a blink, with no evidence to ever show that it happened?
Stephen Hawking invited all future time travelers to one of his birthday parties with this exact thought
And even more importantly, would it ever even remotely be someone's first priority to visit Stephen Hawking's freaking birthday party? What if time travel is such a risk that visiting something that trivial just to prove time travel exists is pointless? Will anyone even remember the freaking birthday party thing in 50 years, never mind however long such a technology would take to develop? Will Stephen Hawking even have the same kind of pop cultural clout as Newton and Einstein in that same time frame?
If you had a time machine, would YOU go to Stephen Hawking's birthday party? Imagine having all of history before you, with the potential for unimaginable risk but also unimaginable reward. You could visit the start of a religion, the age of an extinct species, the rules of a hundred kings and emperors.
Or you could visit the birthday party of one cynical scientist that may not even be a well-known figure in your time, just to stick it to the man.
What I'm saying is "if time travelers don't come to my birthday party then time travel won't exist" is a kinda wonky premise for an experiment.
He was an excellent physicist. That doesn't mean he was a good predictor of human behavior.