No paradox. Someone dropped a hint while looking for whales and nuklear wessels.
So, I have a Star Theory .... well, I have a LOT of Star Trek Theories, but this one is germane to the topic, and it tends to apply to science fiction shows on the whole. IMO.
You can have a time-y wime-y show, like Doctor Who or Quantum Leap, which just kind of has time travel as an accepted and normal part of the show.
Or you can have a science fiction show, like Star Trek or any other show that isn't time-y wime-y, in which case time travel should NOT BE an accepted and normal part of the show.
Now, you can have the occasional bit of time travel- you can have the ever-popular temporal loop for a bottle episode, or you can have some version of the "killing Hitler" problem for an episode (in other words, what do you do in order to ensure the past remains the same), or other minor variations. But the one thing you can't do is have time travel itself become a regular and accepted part of the show- it just doesn't work. It creates way too many problems.
And this brings us to why Enterprise failed so comprehensively out of the gate. It wasn't just the casting. It wasn't just the poor writing for the cast. It wasn't just that terrible, yet somehow ear-wormy, themesong. No- it was, quite literally, the entire plot of the first two seasons was the temporal war. It was such a monumentally stupid idea, even now I have trouble recalling anything about it other than it was really, really stupid.
...this was something, by the way, that DISCO has narrowly avoided as well. NEVER GO FULL TIME TRAVEL.