>MWI still postulates the equivalent of wave function collapse
It's not postulated, but deduced from the Schrodinger equation. MWI is simpler in a sense that it has one fewer axiom. But Occam's razor isn't really applicable here, because it selects from otherwise equal theories, which CI isn't. There are more important criteria to use before Occam's razor.
You can't deduce the Born rule from the Schrodinger equation. MWI can say "look at every basis separately", but you still have to postulate that the probability of finding yourself asking that basis vector (seeing that measurement outcome) is proportional to the square root of the amplitude.
It's not postulated, but deduced from the Schrodinger equation. MWI is simpler in a sense that it has one fewer axiom. But Occam's razor isn't really applicable here, because it selects from otherwise equal theories, which CI isn't. There are more important criteria to use before Occam's razor.