There is no real resistance I think, it's just that the various interpretations are not very relevant in practice. All of engineering that depends on quantum mechanics make do with the standard treatment that has been taught since 100 years now.

The MWI doesn't offer any other way to calculate anything (as it's an interpretation, not a theory). It's a good mental image of what happens though.

I guess at some point there will be some experiment that can be performed that requires a more advanced theoretical method than what current QM provides and then maybe the MWI (or other interpretations) get a chance.