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.
For example, 30 minutes ago a senior director told her entire organization that the primary differentiation in the performance review for the managers will be "quality of communication". Not only this is subjective, but it is not a core performance indicator.
Measuring how "good" your managers is always a hard topic. That's why I found Google's research on it so interesting, since they had both the means and the incentive to run a large-scale study using themselves as the dataset.
I'm not entirely convinced either that evaluating engineers works out that much better. What is the core performance indicator there? Lines of code? Tickets closed? Bugs created? Reputation amongst other engineers? All of those metrics are wrought with perverse incentives. I'd probably end up preferring evaluating managers on "quality of communication" compared to evaluating engineers on any of those.