In particular, extrapolating them from quantum mechanics right now because they seemingly fit strikes me as overly optimistic at best, and drawing conclusions about them is like trying to win the lottery.
Well, first of all, what the Everett-Wheeler interpretation of quantum mechanics predicts are not actually separate universes, but different quantum states of the Schroedinger equation of our universe -- parallel timelines, essentially. Science fiction uses "universe" and "timeline" interchangeably, but they're two separate things. More on this below when I reply to
Edit XYZ.
The existence of other universes might be something completely unrelated to anything we have observed in our universe.
If we're talking about
actual other universes in the sense that Brian Greene was talking about in the final episode of
The Fabric of the Cosmos last week -- other physical realms existing beyond the limits of our universe, having different physical laws and being created at different times -- then yeah, they might be forever beyond the limits of what we can observe and thus would remain untestable. But if one of them formed close enough to ours, it could've left a fingerprint in the cosmic background radiation. So there could be observational data to support their existence.
Apropos 'universes extrapolated from quantum mechanics': the many-worlds-theory fails more than Occam's razor; it contradicts conservation of energy, conservation of momentum, entropy - in fact, you can name almost all fundamental principles of physics here.
And despite all this, it is widely accepted in the physics community.
That's because it doesn't violate any of those things. As I said, it's not actually the physical replication of the universe, merely its subdivision into multiple different quantum states. We know that a single subatomic particle can be in two or more states at once, but that doesn't mean it's more than one particle. It's kind of like overtones in a vibrating string -- there's only the one string, but it's making several different notes at the same time. (Don't take that too literally, because I'm not sure string theory can work as an explanation for this. It's just a metaphor.) But the question is, why is it that when we measure a particle that's in multiple states at once, only one of those states seems to register on our instruments or affect the larger universe we perceive? This is the famous Schroedinger's Cat paradox -- the radioactive atom is both decayed and undecayed at the same time, but the poison capsule it triggers can't be both triggered and untriggered at the same time, so the cat can't be both alive and dead at the same time. So why isn't it? How does the multiplicity of states on the particle level end up producing a single overall state on the macroscopic level?
The Everett interpretation -- more properly, the relative state formulation -- says that it's a matter of correlation. As other particles interact with our "hero" particle, they become correlated with one or the other of its states. If an experimental apparatus (whether a cat in a box or some more standard form of detector) measures only one of the particle's multiple states, that's because the states of the particles making up the apparatus have collectively become correlated with that state instead of the others. But those other states of the hero particle still exist, and they can have correlations too. The "Many Worlds" idea is that all the particles in the ensemble are in multiple states at once, but those states are sort of aligned with each other into a set of mutually exclusive correlations, which means that the overall macroscopic ensemble -- the measuring apparatus and the universe it occupies (or at least as much of the universe as it interacts with) -- is in multiple distinct states at once too. And because the particles in those states are correlated only with each other, the states are isolated from each other, non-interacting. And those are what we mean when we talk about parallel timelines. The particles making up the universe haven't been duplicated; the timelines are just different macrostates of the same single set of particles. One universe existing in a superposition of histories.
Also, a lot of physicists don't actually believe the "parallel histories" represent physically real universes. They see them as a mathematical abstraction. Others believe they are genuine alternate realities. Either way, though, there is significant experimental support for the Everett interpretation. It works as a theory explaining and predicting quantum phenomena, in particular for explaining how quantum multiplicity seems to resolve into a singular classical reality.
(Although I'm partial to a new variation on Everett called Quantum Darwinism, which has already gotten some experimental support. The idea is that as particles interact, the different states "reproduce" by creating correlations in other particles, and the states that are most stable "outcompete" the others and spread farther until they bring the whole system into correlation, while the other states don't spread as far and just fizzle out. So instead of a bunch of coequal parallel histories, you get one victorious history that represents what we see as reality and a bunch of potential histories that didn't end up actually "happening." However, it seems to me that this allows for the possibility of at least
some alternate histories, since an evolutionary process can branch out into two or more "species." If two competing states happen to be equally stable, that could potentially produce parallel histories, although they would be far fewer than in the standard "Many Worlds" model.)