Of course, a good manager could add more value than the people she manages. Engineers can fail to appreciate all the fuzzy unmeasurable people-stuff it takes to keep a big team communicating and working together.
Mediocre managers probably don't, which implies they should pay themselves less than they pay the engineers that report to them. Seems like a problem that's unlikely to be solved.
People become unproductive for many reasons, maybe they just didn't keep their skills current, maybe they are disillusioned, maybe they weren't ever that useful to start with and got the job by other means. But such people are impossible to fire under normal circumstances. So a good manager "promotes" them to some meaningless post to get them out of the way. Then that manager leaves or moves, and someone who doesn't know the score comes along and decides that hmm, maybe the VP of Paperclips could be reassigned to VP of Operations. And now we have an utter incompetent in a position of real power.
Engineers? What are you talking about? My dad's an engineer and he knew how to appreciate all the fuzzy unmeasurable people-stuff. He communicated with multiple departments and kept things running as smoothly as he could. He dealt with salespeople without going crazy too! The only value added by his bosses is that they gave him enough room to do the things.
Oh wait, you mean "engineers" as in "software engineers"...well then you're just continuing the stereotype of programmers being socially inept.
I'm a "software engineer". I said can to try to hint that sometimes someone who's an expert at one thing, who, unlike your dad, happens to not be an expert at a second thing, fails to appreciate the challenges of that second thing, and that general pattern can specifically cause an illusory case of the issue described by the OP.
Mediocre managers probably don't, which implies they should pay themselves less than they pay the engineers that report to them. Seems like a problem that's unlikely to be solved.