There is a great book called "Management by Baseball." The author of the book points out that baseball managers are typically former players, and they usually believe that the most important position on the team is whatever position they used to play. I doubt PMs regularly make more than engineers across all levels at all companies, but in general the outcry you are seeing about this isn't limited to engineers. In my experience, almost everybody at almost every company thinks the thing that they do is the most important.

I can tell you that I have worked in 4 major roles: - engineer - sales engineer - business development - CEO

In my experience, the pay is directly tied to the need of the position to manage uncertainty and ambiguity, and evaluate difficult risk/reward tradeoffs. As you move up the hierarchy, you do more of this.