I just saw the fantastic Everything Everywhere All at Once which was a truly brilliant variation on multiverse themes, and remembered that I think I'd first encountered the trope in RAW's Schrödinger's C at trilogy.
The idea (from Max Tegmark) that physical existence is the same thing as mathematical existence, or IOW that the only thing that exists is mathematical structure, and all mathematical structures exist. So it's a type of multiverse theory.
It's an idea both disturbing and liberating. It cuts against our most basic experience, and a sort of iron law of reality – that the world is a certain way, and that the future will be a certain way, whether or not we have freedom of action to try to affect it. It is an acid bath that apparently dissolves the iron bars of reality.
Consider the idea of quantum suicide – which, if you took it seriously, would be a very powerful technique to achieve almost anything. Want to force a fair coin to come up heads? Flip it and kill yourself if it lands tails – voila, all living versions of yourself have gotten heads, congratulations. Or if you don't trust your future selves to carry out this plan, you could rig a machine to do the killing automatically.
I've had a couple of near-fatal accidents which have almost convinced that this is sort of how things work – most versions of myself are dead, but of course the version that is writing this right now is one of the survivors. I don't feel immortal, and I have no desire to test this theory by engaging in further risk-taking.
While it might be pleasant in some ways to think that there are other worlds where versions of me are enjoying different activities and different fates, it's also the ultimate in nihilism. If every possible world is equally real, then really nothing matters, except locally. The vastness of the physical cosmos we can observe is nothing compared to the vastness of possible states of the cosmos, so our precious single-threaded existence is even smaller than it was before.
Conclusion: there is something deeply wrong with the multiverse idea, but (and this is crucial) there is also something deeply wrong with the default commonsensical single-universe model of reality that we usually employ.