In my experience, pay rarely has any kind of correlation to the amount of work being done. I see it merely as a pay for responsibility for the work of those under you or, more succinctly, "being paid to throw yourself under the bus in lieu of anyone you're managing".
Correct. In addition, sometimes advocating for those under you is a sacrificial act, because you're putting your reputation on the line.
It sounds like the management philosophies at our respective orgs are very different.
I think that's the point, you wouldn't see it. If a good manager gets unreasonably or unfairly reamed by his boss, he's probably not gonna tell his team about it, because it would be a blow to morale. If it was indeed the team's dysfunction, he'd try to improve it.
Meanwhile the most useless people are failing upward into CEO.
It's rare, but it does happen.