Then there is the closed loop, like in Harry Potter, which makes lots of sense, but allows for some paradoxes and negates free will. Also, alternate timelines can’t exist.
What paradoxes does it create?
Harry can cast the patronus because he saw himself casting a patronus. This breaks causality.
He saw himself doing it, and it gave him self confidence that he could do it. It is not that he can cast the patronus because he saw himself do it, it is that he can cast the patronus because he has the ability and knew he had the ability because he saw himself do it. I don’t see the problem.
What came first? His patronus or his confidence?
Having seen the patronus gave him confidence, but he needed confidence ni the first place to cast the patronus. These two things are causing each other. In the context of the story, that’s perfectly fine, but giving up causality like that would make this mode of time travel unsuited for Star Trek.