If you really want to rattle the cage, try a ST campaign without transporter technology. To me, the transporter was far less likely than warp drive and the other tech, and the writers misused and abused it terribly.
I agree, but I think transporters are a distinctly Trek element, and most fans associate it with the franchise. "Beam me up, Scotty", and all that.
I think the issue is a distinctly RPG one. We expect players to solve problems based on the situation. Trek has lots of examples of crazy things happening due to time travel or transporters or replicators, and so the players who are familiar with trek are going to expect they can use those techs to solve problems. In a TV show, the writers can just ignore the implications, but a GM can't.
And then if the GM introduces any crazy tech of their own, they're going to have to deal with that.