And I would argue the difference between a mediocre manager and a good manager is more than that.
You seem to be assuming that there is an equivalence between good programmers and good managers?
I wish I lived in this alternative reality you describe. My career has been littered where non technical managers--essentially clerks--get paid more than I do to sit around with a others and talk about what should be done while I (and colleagues) do all the doing. I end up doing a LOT of "managing" from behind the lines in all these cases.
Frankly, the reality distortion field where "a good manager has increased the output of their team" has been such a small observed sample, that I wouldn't be able to claim there was even a correlation between the two, much less causality; I'd just chalk it up to something like "the water" or "the lighting" if I saw it happening with any regularity.
(QuickJS seems tres cool; hat tip to the author)
That's a nice economics just-so story. But do people think that the median manager is effective? I'd say less than half of my managers have been effective. Some of them even got promoted.
If you make a PR and it gets left to die after a few days, who cares? If someone keeps an eye on it and tells you what they're looking for with a smile, you're going to try and get it done.
Good managers increase the output of their team, bad ones try to make themselves look the best.