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IMO, the perceived inscrutability of quantum mechanics is mostly the result of the dominance of the "shut up and calculate" approach to the question of interpretation.
Don't get me wrong, I understand why focusing on the math and ignoring the rest is a good approach to have when you're actually doing practical scientific work in the field. But if you're wanting quantum physics to "make sense", then you're asking about what it actually says about the underlying reality, and that's a question that requires thinking about interpretations of QM.
Once you start thinking about it in terms of a particular interpretation (or category of interpretation), then QM makes as much sense as any other high level physical theory (certainly no worse than general relativity.)
The various interpretations help in processing the math, but isn't the same as understanding - there are a bunch of fundamental facts about quantum mechanics that we just don't understand, even though we know the elements exist, that they happen, and even how we can take advantage of them.
The difference between quantum mechanics and other high level theories like relativity is actually quite large, because the higher level interactions all derive from quantum level states and interactions. At the point where question marks really start popping up (weak and strong nuclear forces, gravity, dark matter &/ energy) it's almost always a matter of quantum mechanics getting involved and being weird.
My quantum mechanics professor started our first lecture with "if you think you understand quantum mechanics you do not understand quantum mechanics", because there are still some really big question marks around our understanding of it. Especially what in the fuck spin actually is.
The various interpretations help in processing the math
In the same sense that the territory helps in processing the map, I suppose.
but isn't the same as understanding - there are a bunch of fundamental facts about quantum mechanics that we just don't understand, even though we know the elements exist, that they happen, and even how we can take advantage of them.
I'm not sure what you mean here; discussions of interpretation are literally about understanding these facts.
The difference between quantum mechanics and other high level theories like relativity is actually quite large, because the higher level interactions all derive from quantum level states and interactions. At the point where question marks really start popping up (weak and strong nuclear forces, gravity, dark matter &/ energy) it's almost always a matter of quantum mechanics getting involved and being weird.
Going to have to disagree with you here, relativity, both special and general, get just as weird without any need to invoke quantum physics. And they're not the only one. The only difference is that we have a general consensus on how to interpret them, which we don't with QM.
My quantum mechanics professor started our first lecture with "if you think you understand quantum mechanics you do not understand quantum mechanics", because there are still some really big question marks around our understanding of it. Especially what in the fuck spin actually is.
I think this is equivocating a bit; there is a difference between the things we don't understand about quantum physics, and the things we just straight up don't know. I think it's possible to understand quantum physics, with the caveat that understanding means recognizing that there are things about it that we simply do not know.
I think a degree of shut up and calculate is needed, at least in the beginning. Without a solid math based understanding of the fundamentals, trying to prognosticate on the ‘meaning’ of it is inevitably going to fall into pop-sci style stuff. You’ve gotta know what you’re dealing with a little.
I'm not so sure. I think a degree of shut up and calculate if you actually want to get a physicists level understanding, a large degree. But I strongly believe that it's no harder to give a clever layman a working understanding of the underlying concepts, in purely conceptual terms. Honestly, I think the reason the quantum mechanics has been so prone to pop-sci charlatans is that legitimate science communicators keep trying to explain it in interpretation-agnostic terms, which makes it sound far more mystical and paradoxical than it is.