I think a manager of people cannot feasibly manage more than three dozen. And we're talking truly gifted at that level. Thirty plus directs under active management – I’m not sure where the time to do that would come from (thus the truly gifted bit). I’d expect a competent manager to be able to work with about a dozen or fifteen independent-minded folks and a talented or seasoned one up another six or nine. I think it’s safe to say that a manager, even a green one, who is not able to handle less than a dozen is in the wrong line of work. A manager of people with fewer than six directs should be able to lavish attention on them. That manager should be facilitating those people’s successes with grace and largess. Grooming them or training them, or perhaps it's a hybrid people manager / expert skill practitioner role.
Maybe being a manager is a similar to being a teacher in the need and amount of rationed attention. Or a waiter. That's an interesting notion. In the standard business-as-a-kitchen metaphor, I typically hear managers cast as line chefs. But that's completely wrong! Line chefs are expert practitioners. The wait staff moves between diners and kitchen staff, pacing the kitchen work and upselling or downselling to keep the kitchen effort on keel.
I'm going to have to put that in my brain and shove it somewhere near the top.