@fohjoffsAs the author of a do-over, I do think about this stuff, and I have opinions. They differ considerably, but some might be interesting, so ...
In my case, there is no 'pure time-travel.' The MC 'moves' from a future date to an earlier date, but there is an accompanying change of universe. The universe the story is set in is, definitively (and clearly, very early on) not the universe of his first life.
Does that many the physics possible? Maybe, or maybe not. It doesn't violate causality, because nothing he does can affect his own future. His original universe is off doing its own thing and never the twain shall meet.
Beyond that, my characters are certainly interested in the question of why and how this happened, but they have no more idea of how to answer that than anyone else does, nor does the story rely on there being a non-supernatural explanation.
On this point:
A reasonable rationale for a DO does NOT include
- correcting stuff you screwed up
- another chance because you were screwed over
- a reward because of your 'valiant' death
Why not? Who and/or what defines 'reasonable'? Obviously, if the 'why' is some 'blind' piece of physics that allows for both time travel and de-aging, or for the transference of a 'soul' and 'memories' from the future to the past, that just 'happens,' sans rationale. But any supernatural do-over might indeed have an agent that intervenes for any of those reasons.
Consider a hypothesis. This is absolutely not canon for my story (not even close), just a thought experiment.
Imagine everyone gets a do-over. Every single person. Given an infinite number of universes and a non-infinite number of sentient beings, this is theoretically possible. By whatever rules are established, everyone gets to 'reset' to some point (chosen by whatever means) and try again.
Now, if we presume an intelligent agent, consider modifying it so that it's just every single person who, by some set of criteria we are not aware of, lived a 'significantly sub-optimal life'. Someone who, on balance, loved their life, or who loved everything up until, say, 60, but made a horrible choice then, would hate starting over at a young age and desperately having to try to not squash butterflies left and right just to get to a 'better' life. So, in that sense, giving someone who didn't want one a do-over might be torture, not reward. And our intelligent agent doesn't want to torture people.
Or, consider another do-over hypothesis. Maybe we really are, all of us, living in a simulation. Those running the simulation save the state of one or more characters in the simulation, boot up another simulation (perhaps with slight tweaks), and plop the saved-saved characters down in the new simulation at an earlier age. Entertainment ensues! Years of fun for those running the simulation!
Or maybe we aren't, but the do-over world is a simulation, created by super-intelligent beings who can 'sample' the state of the world in e.g. 1980 and kick off a simulation, but use the state of one or more persons from a later time in their new simulation.
You can go on and on with this. Given sufficiently advanced technology, anything can look like magic, including do-overs. Maybe it's 'Riverworld'-ish. Superadvanced beings build Earth 2.0 circa 1980 and inject the captured state of various people from later for their own motives. What, you say? They can't do that, because the stars and constellations will all be different in some other time? These are super-advanced beings. Their Earth 2.0 accounts for that, and - in the world they've built - the entire history of the Earth is carefully edited so the constellations, location of the Earth within the universe, etc are all consistent.
In those last few examples, the 'reasonable rationale' is 'entertainment value', and is entirely external to those experiencing the do-over. They have the technology to do anything they want with little effort, so firing up a new model and watching it go is a fun diversion.
In my case, at least, I see actually explaining any of this within the story as undermining the narrative. We don't know why this is happening. The characters don't know why this is happening. They are just reacting to a situation in the best way they are capable of at the moment.
While looking at a similar question, I ran across a quote from the original author of 'Groundhog Day'. Paraphrased, he said he struggled for a while with 'Why?' and 'How?' In the end, he dropped those, and he felt it was the right choice, making the story much more relatable to the audience. None of us really know 'why' or 'how' we are here. We have theories that seem likely, but - as a physics professor of mine said decades ago (and as is still true), there are points within the physics-based model of the universe at which the best answer we have now is 'And then a miracle occurred'. You can call this the Anthropic Principle, but that's shorthand for 'We don't know why the heck a number of fundamental constants just happen to have values that support intelligent life. They just do.'
One more note: it's not on SoL anymore, but the story 'Magestic' (spelling intentional) postulates a series of nearly identical universes running in parallel to each other, but offset in time. Someone going from Universe A in 2020 to Universe B in 1980 isn't traveling in time, because those are simply the times at which the universes currently exist. Magestic postlates bodily transfer (and, thus, the person transferred must kill 'themself' in order to take on their identity), but one could do the same thing with information transfer. If so, one can further postulate a series of non-identical (but highly similar) universes with offset clocks allowing any arbitrary number of people to get 'do-overs' by moving 'sideways', not 'backwards'. Implicitly, of course, overwriting the 'soul' and memories of the person who was there before the 'do-over' kills them, but the person experiencing the do-over has no agency in that, and any external agent might choose a time when the 'victim' was essentially already dead, repair the damage, then perform the transfer.
Like I said, I think about this :) And nearly all of that discussion itself would fit in the story, and might turn up there, because the characters certainly care about why this happened and what it all means and if there's a motive behind it all and so forth.
But any answers will likely take a long time to appear (if ever), because they have to actually add concretely to the narrative, and there's something of a history of do-overs that go off the rails at the point someone inserts 'meaning' into the story. Not all of them, but it's happened a fair number of times. The physics-based one to which you refer is an exception, but that's 'baked in' at the start, and the MC is in fact the intelligent agent who caused the whole thing in the first place.