I'm a chemist; we actually have to use quantum physics on a routine basis. The main reason many-worlds never got traction is that it doesn't make a testable prediction. Most physicists realize that making a model of reality that predicts experiment (as far as possible) is, well, science; BSing about what the implications are is more of a late night and beer thing.

In other words, if the model implies that there may be other worlds, but they can't conceivably be detected, then who cares?

One last thing: there's some pretty good evidence of nonlocal physics these days. It's inconsistent with general relativity, but no biggie. We already knew that general relativity and quantum physics were incompatible. The current situation in physics (for the last 30 years or so) is considerable confusion at the level of fundamental theory, but extremely robust models for every actual physical situation that we can probe. The robustness of the models is exactly what has halted progress.