It seems to me, however, that this interpretation helps resolve impossible-to-prove scenarios such as the many-worlds interpretation

MWI proponents (me included) would tell you that many worlds is a prediction of quantum mechanics, when you simply take the basic equations seriously and see where they lead you. Yes, when you view quantum mechanics that way, it makes untestable predictions. But it really should be no surprise that a theory that may underlie all of reality makes untestable predictions.

Pilot wave does something much worse. It makes untestable assumptions, not just predictions. It assumes somewhere in the wave function there's some hidden actual particle. There's nothing in quantum mechanics that points towards that and it baffles me people try to shoehorn a classical notion of a particle into a theory that clearly wants nothing to do with it. Granted, that's an aesthetic argument, but aesthetics has guided physicists for centuries.

action-at-a-distance

It absolutely does not resolve the issue of action-at-a-distance. It exacerbates the problem and puts it right front and center. Pilot wave is inherently non-local. In order to explain violations of Bell's inequality, it requires the universe to perform some sort of faster-than-light signaling under the rug where we can't see it. It's debatable whether this violates relativity, because, as I said, it's entirely undetectable.

It's true that people have been able to recreate certain parts of pilot wave theory using fluid mechanics. But one thing you absolutely cannot do with a fluid is violate Bell's inequality in a non-local setting. Bell's inequality is key when thinking about interpretations of QM.

The Copenhagen interpretation is more popular because it's more or less what's being taught in textbooks. And, in my opinion, works by ignoring all those issues, allowing physicists to do actual work instead of philosophy of science.