I also like your thinking trott. The idea of “banning” Time Travel has already been dealt with in fiction. I can’t remember the author, but it appeared in one of the Hugo Annual Anthologies.
The premise is, if you have a machine that can travel in time, you can just as easily use it to simply “see” into the future (or past) without having to actually travel there.
You can set it to whatever period you like. 1 million years from now. Or 100. Or even 1/10th of a second from now.
Why would you choose this latter setting? Why, to see into your neighboor’s bedroom of course. 1/10th of a second into the future is virtually like being there now.
This is why it was banned.