Fixing the timeline sounds disrespectful to its inhabitants. What if things are good, if there are new people or previously existing people who survived in that timeline? You can't just unexist those!
How would you even know if you're the main timeline? Is there even such a thing? Isn't every universe (but one) an offshoot? Or do timelines only count as broken if a future has been established but something was changed in the past?
That case would be bad news for the post-Endgame MCU and my preferred X-Men timeline. For this Loki as well. Would that mean he was recruited to eventually unexist himself? Soooo... what if he destroys the TVA and lets the multiverse roam freely, which might result in weakening the walls between dimensions?

Oh, hey, what if Loki fucking with the TVA is what messed with time in the X-Men universe? That would be hilarious. And helpful, because I'd like that problem to be explained away somehow.