A simple counterexample is superdeterminism, in which the different measurement outcomes are an illusion and instead there is always a single pre-determined measurement outcome. Note that this does not violate Bell's inequality for hidden variable theories of quantum mechanics, as Bell's inequality only applies to hidden variables uncorrelated to the choice of measurement: in superdeterminism, both are predetermined so perfectly correlated.
Just to be clear, where in the Schrödinger equation (iħψ̇ = Hψ) is the "multiverse"?
Copenhagen interpretation is just "easier" (like oops all our calculations about the univers don't seemt to fit, lets invent "dark matter") when the correct explanations makes any real world calculation practically impossible (thus ending most of physics further study) as any atom depends on every other atom at any time.