MWI doesn't require that every imaginable reality actually happens; it just says that many of them happen. And of course the laws of physics and probability still apply; only things that are physically possible can happen, or things that can validly result from a given set of circumstances. There are lots of possible timelines that can be imagined but that couldn't actually happen without violating those parameters.
It may be unsatisfying but it sure as hell makes more sense than Voyager's time travel mechanics. Universes don't pop into existence when they branch. Pre-existing but overlapping timelines simply diverge.
Err, no, I don't think that's how it works. At least, not in the sense you mean. In any case, the distinction is irrelevant on the scale of personal experience and events, because we're still talking about a history that was identical until Nero came back, and that's very different from the Mirror Universe, which was different from a far earlier point.
Lol - yes I don't disagree with any of this, although in theory, there could be universes with different laws of physics, no matter how improbable, or at least universes where the physical properties of the universe are different, even if the same laws of physics are underpinning them.
Voyager's time travel is not what I personally mean when I talk about MW1 but many people do believe that a branch 'pops' into existence when a divergent event occurs and can be overwritten if someone goes back in time and 'rewrites' that divergent event. I'm still not 100% clear that I understand what Voyager was doing with the temporal police or the Krenim temporal incursions.
I've always viewed it as the viewer simply jumping tracks with the time traveller and becoming part of the history in the 'new' timeline.
In fact just because Spock Prime has a history identical to TOS Spock does not automatically mean that he IS from the TOS timeline any more than Mirror Spock Prime.
For all practical purposes they are the same (unless you are a dimension hopping Klingon I suppose) but a lot of people get worked up about this sort of thing. It's analogous to the transporter as a kill and clone machine I suppose. Alternate versions are different people and in some cases, they won't even be genetically the same, such as NuChekov, and maybe even Kirk's blue eyes if you want to be really pedantic.