> MWI is arguably the simplest interpretation from the standpoint of rule simplicity: it doesn't involve a notion of collapse, so it has less rules than other interpretations.

This isn't entriely true. MWI still needs to explain why the observed behavior of a measurement is non-linear. So, it comes with a rule about how to deduce the observed probabilities from the wave function amplitudes: you have to do the calculation in a single 'world', you can't do them for the entire wave function; and then the amplitudes give you some kind of count for each 'world', so that if we then perform an analysis on all observers in all worlds, the chance of us being one of the observers who measure state A is proportional to the amplitude.

Even worse, the MWI needs to find or posit some way for the universe to choose, for each quantum measurement, a particular basis that gives rise to the many worlds - as that is also something missing from the Schrodinger equation. The CI has an advantage here, as the basis is explicitly chosen by the measurement device, whereas in MWI it has to be a fundamental property of the universe (this is usually suggested to happen through de coherence, that there is actually one unique 'right' basis, the one that is stable under de coherence effects, but this is not entirely satisfactory).