> I'm honestly a bit surprised that no one makes this argument in favor of the many-worlds interpretation of quantum mechanics, as it's the only theory which accounts for all experimental evidence while not forcing us to invent a mechanism that "eliminates" the many realities that we don't want to accept, while in fact they arise naturally out of the theory.

I think you're projecting the existence of these worlds. Certainly you could view the equations that way, or you could view the particles as fundamentally real and obeying a non-classical law of motion, as in de Broglie-Bohm, which was actually the first the interpretation to correctly account for measurement.