For me, it falls squarely into the category of "if that's what helps you sleep at night...".

Taken on its own, I don't think it's a very satisfactory answer...but I also think that a lot of the discrepancy issues aren't every interesting questions, so it all washes out in the end.

It just means Annorax wasn't as crazy as he came off to be. Which stands to reason, considering all he accomplished. Perhaps anthropomorphizing time is legitimate in this universe.

As a general rule, unless given an explicit explanation for discontinuity on screen, it should be the explanation of last resort.

The problem is that as an explanation it can be used for everything. Consider any shot production error that might happen. Actually let's use one of my favorite TNG episodes for discontinuity: Parallels. In the final scene of Parallels, there is a continuity error, where a bow switches sides.

Does this mean we should perform an inception style deep dive and say perhaps Worf is still jumping universes? Could we use this to, in fact, explain ANY minor production error?

I mean we could. But that's probably not what's intended by the authors.

For example I am very much a fan of the idea that early in TNG's run the Ferengi still valued gold and later on they do not, and this matches up with better and better replicator technology eventually being able to create gold at scale. But also, maybe it's just temporal discontinuity.

Can we reconcile Picard's relationship with his mother with what little we see from TNG and what we see in ST: Picard? This can be a fun exercise. But we can also say "Eh not the same Picard."

The idea that Khan is destined to happen is a heads on explanation for the intractable problem of Star Trek is rerooting its history into our modern history. Star Trek is, after all, a vision of our future and that vision has changed from the 1960s. This is a change designed to add some meaning to the show.

On the other hand, if "time pushback" is used to explain anything and everything on the show, it runs the risk of becoming flat out meaningless.

So when would I consider it an acceptable explanation? Whenever it's given as the explicit explanation, or maybe if there's a very clear connection.

It does raise an interesting question of whether a similar time-pressure might also be responsible for things like parts of the Mirror Universe coming in sync, since the alternative is that it is either a massive coincidence, or a someone else meddling.

Personally, I'm ambivalent about it. It has some interesting implications, with fate and whatnot, but at the same time, it wasn't really necessary, and seems like it would introduce a whole load of problems.

If events automatically converge, why was there ever a time war?

It also raises the Doctor Who type question of what happens if someone with knowledge of the future makes it impossible for those events to occur at all? Does the universe resort to increasingly supernatural means to achieve the same end, or break entirely?

I don't hate it. It makes room to tell new "old" stories without just completely dismissing canon. The idea of a "fixed point in time" is a concept that I think originated with Doctor Who. The Strange New Worlds concept is similar, but instead of a fixed point its a fixed event or fixed outcome.

I do wonder though, how much of this "time pushing back" is actually that? Or is it actually just the "Federation Time Cops" from the far future making sure things happen even if someone successfully meddles with history. I actually kind of hate the concept of time travel being a thing in Star Trek. Leave it to shows like Doctor Who.

The butterfly effect is overcome by something in Star Trek. But what characters perceive as time 'correcting itself' or 'pushing back' may be an emergent property of whatever mechanism allows them to manipulate events outside the constraints of normal spacetime in the first place. I'm not even sure the math involved in chaos theory applies when operating non-linearly. Math and physics nerds; Feel free to correct me.

I'm also not sure that Anarox's perception of time as having moods or intent is correct, but it may be useful to believe and act as though it does, in lieu of an explanation that is not forthcoming, even in-universe.

The whole "River of Time" and "Set Events" and "Destiny" in Time Travel goes back to..well forever. And it has already been part of Star Trek from TNG on.