Earlier quoted context omitted.
Compare your best manager and your best engineer, and the manager _does_ contribute multiples more than the engineer does. You take this to the extreme, and the best CEOs in history have added additional billions in value to the companies that they've helmed.
Anecdotal evidence tells otherwise :) Not kidding, in all the companies I worked for, the best engineers were way better contributors than average managers. Just consider that in many companies management is badly hit by diversity targets, they forcibly promote people to meet these targets and competency suffers.
And then if we're talking about technical managers and not just CEOs, the literature there is even more limited, since most middle-management in the past has been of known repetitive tasks, rather than more variable more creative work. And it's not like there are schools that can spend four years teaching you how to be a good manager. MBA programs tend to care more about the details of running a business and let the people aspect figure itself out.
So maybe an analogy might be, if all the engineers you hired were self-taught, and if you only had one engineer assigned to each team. Then maybe your average quality of engineer would match your quality of manager.