I brought this up elsewhere in this thread, but the fact that quantum mechanics and gravity are not reconciled suggests to be that even Schrodinger's equation does not fit the evidence. The "low-energy" disclaimer one has to add is very weird, maybe weirder than any counterintuitive consequences of quantum mechanics.

It's not the Schrödinger equation alone that gives rise to decoherence and thus many-worlds. (Read Good and Real for another toy model, the "quantish" system.) The EPR experiment and Bell's inequality can be made to work on macroscopic scales, so we know that whatever mathematical object the universe will turn out to be, it's not going to go un-quantum on us again: it has the same relevant behavior as the Schrödinger equation, and accordingly MWI will be the best interpretation there as well.