I have known about MW for 25 years or more, thanks to popular science writers. I don't see it getting more traction than it already has absent some way to falsify it. It's stylish from a distance, but like imaginary numbers, you should tidy up your multiverse when you are done playing with it.
That's a common criticism, but many-worlds is a consequence of a theory, not a theory itself. Plus all the other candidates are worse. (And Copenhagen isn't really a theory at all since it never gets around to defining what a 'measurement' is.)
Many worlds requires postulates (Everett's word!) that are not a consequence of theory, in particular that the wavefunction is an objective property of a particle. This is very much in dispute, and is rejected by the ensemble interpretation, consistent histories, etc.
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.
