I don't agree that those interpretations are inferior to MWI. In particular those theories postulate that the world is essentially probabilistic, and so do not have MWI's trouble with predicting probabilities.
well, to me it actually works in the opposite direction, like prove by contradiction - if the Many Worlds is the best/logical/natural consequence of the indeterministic view of QM than the indeterministic view is definitely have to be overturned.
All the Bell experiments i read about so far have obvious gaps allowing for obvious explanations. And if you take the latest one, the heralded loop-free, then there is obvious question - why didn't they published the statistics of the unconnected, non-entangled runs? I mean it is obvious from current QM orthodoxy that non-entangled runs wouldn't produce S>2, yet from alternative, locally-realistic, experiment result explanations the S>2 would be produced in that case too (the S>2 isn't possible in the locally realistic world, yet it is possible to locally realistically explain S>2 in all the Bell experiments that so far i've seen)
If you're interested other reasons the MWI is often considered "nice" is that it is: linear, local, causal, realist, entirely unitary and in some sense (this is often disputed) minimal. Other interpretations have to add mechanisms (for example wavefunction collapse) in a rather ad-hoc way in order to stop many worlds happening.
Many worlds is by far the best hypothesis to date.