And the Q I forgot. Actually, the Q are already in charge to make sure "all of creation" isn't destroyed. So any human attempt to "control" the timeline can just be snapped away anyway. I think there's even a novel about that, where Q takes Picard on a ride to stop the universe from being just ended by a greater power.
Isn't this episode a dramatization of the double-slit experiment, wherein the anticipation of a specific result produces the action that creates said result? In this case, Braxton's crime is anticipating Janeway getting her comeuppance.
Yes. The Novel "I, Q." God decides not to end the Multiverse because Q made "her" laugh. It also includes a hilarious scene where Q doesn't understand the difference between a queuing line and a "Q" line.
Then again, the TIC aren't so much acting as "time police" in this episode as they are preventing one specific disaster - the destruction of Voyager. We don't really know what their attitude is towards time in general. Maybe they are mostly reactive, like the Department of Temporal Investigations. And even if you think that the 29th-century TIC is not realistic, I'm hoping more people agree that the DTI is. If you don't think the TIC is needed, the DTI at least must be.