A multiverse with independent universes and varied physics seems plausible given the physics of inflation. On the other hand the quantum kind has multiple parallel worlds. That should have different versions of ourselves among everything else that is possible, but seems unprovable and inelegant as a solution.
The main issue with MWI is that we don’t see the quantum state. You can’t even assign the quantum state to a particular location in space. It’s not like a field that has well-defined locations even if you can’t see it. Strangely, the quantum state cannot be pinpointed to even exist at any location at all, and seems entirely independent of the physical system it’s describing, yet if you evolve it mathematically it statistically predicts its behavior accurately.
MWI then claims that maybe reality is actually the quantum state, but like I said, the quantum state is not visible and almost seems to have no connection to our actual reality, so you by extension are then claiming everything we actually perceive in the real world must not actually exist, and the thing we cannot see it at all must be reality. How does that make any sense? Clearly we see the world. MWI proponents will chalk it up to everything we perceive being an illusion created by the conscious mind, and so it will be unraveled whenever we unravel “the mystery of consciousness,” but then they just end up shifting one mystery under the umbrella of another.
Tim Maudlin has a good lecture on this whole problem:
https://www.youtube.com/watch?v=us7gbWWPUsA
It seems to me unavoidable that either the quantum state is something physically real that exists alongside our normal everyday reality, or it doesn’t exist at all and is just a tool for logically accounting for states of the universe that are disallowed by its structure. But to state everything is the quantum state does not particularly make much sense because then you are left with no explanation of the world we actually perceive at all.