Another quote:
By these standards, the ontological commitments of the multiverse or the many-worlds interpretation are actually quite thin. This is most clear with the many-worlds interpretation of quantum mechanics, which says that the world is described by a state in a Hilbert space evolving according to the Schrodinger equation and that’s it. It’s simpler than versions of QM that add a completely separate evolution law to account for “collapse” of the wave function. That doesn’t mean it’s right or wrong; but it doesn’t lose points because there are a lot of universes. We don’t count universes, we count elements of the theory, and this one has a quantum state and a Hamiltonian. A tiny number!
I agree with all that (except for "and that’s it" part for MWI, given that the Born rule is still a separate assumption).
Counting worlds or universes towards complexity of a quantum theory is as silly as counting species towards complexity of the theory of evolution.
If it's worth saying, but not worth its own post, even in Discussion, it goes here.