And that's fine, but the idea that this is simpler than a theory which says my experience is a reasonable reflection of reality, is not. Occam's razor is not about number of equations, it is about what is simplest. I experience a single "me". A theory which supports that experience directly and obviously is simpler than a theory which does not.
This is particularly true when the "extra" equations are simple and obviously a part of the other equations.
The reason why this all gets so convoluted is simply because it exposes how much we rely on terms and concepts that are defined very fuzzily, and often aren't even defined at all, but just accepted for granted as if everyone means the same by them. And then it turns out that we don't, which should really come as no surprise.
The "indistinguishable" part happens because, according to Everett, there is some version of the experimenter that will have the same experience as the single experimenter in the Bohmian world.
This is not simpler. I have no reason to believe that there are infinitely many copies of me out there. Everett's theory says that there are. Fine. I can't disprove it. I also can't disprove that every instant of my experience is being carefully orchestrated by a thousand angels. It is experimentally indistinguishable from any theory you care to posit.
But I prefer theories where my actual experience is supposed to be a reasonable reflection of reality. I experience a single me and therefore I would prefer a theory in which there is a single me. Bohmian mechanics provides that and in a completely natural and reasonable way.
Everett categorically disputes my experience as being reflective of reality. There are infinitely many copies of me and my experience of being singular is an illusion. I can't dissuade people from embracing that, but it certainly strikes me as peculiar.
Also, in terms of experiments, Everett has infinitely many copies of the universe where all of the statistics of the experiments come out wrong. There are infinitely many that come out right. Is that experimentally indistinguishable? I don't know. Kind of a strange question in the context of "most everything happens".