Programmers tend to think that programming is the most important part of making software. However, managers think that managing is the most important part of making software, and business analysts think that defining business requirements is the most important part of making software. Asking a room of programmers about the value of business analysts is going to result in feedback that is heavily biased. As you say, we've invented a narrative of moral superiority, and it's a seductive one.
I suspect programmers are less correct in their assumption than they would like to believe. Probably more correct than the other two groups of employees, but still less than correct. The sad fact is, most programmers (especially non-entrepreneurs) don't "get" what PM's and BA's do, the same way that most managers don't "get" what programmers do, but their role still provides value (if they're good at their job). The nature of their job often involves filtering crap for their programmers, so the better job they're doing, the more invisible they look.
The value PM's provide is enabling specialization of labor. They act as the interface between business stuff and tech stuff--translating business requirements to tech requirements for their programmers, and tech trade-offs into business trade-off for their stakeholders. It's something that programmers can do themselves (especially entrepreneurial ones), but taking that work off their plate lets them focus on technical matters.
Of course, the above is a perfect world, which is about as common as the mythical sufficiently-smart compiler. Which is to say, it never exists and never will. Nonetheless, there are such things as PM's that provide value. My experience is that ones with non-negative value are about one-in-four, ones with measurably positive value are less than one-in-ten, and if you find one you should pay what it takes to keep them around. YMMV.
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That said, there are reasons why PM's are paid more than their value more often than programmers are. I agree with the majority of these, but I'm restricting my contributions to the portions of my opinions which aren't echoed throughout this thread.