Player-coaches are a real thing, but noticeable because of how rare and unusual they are. The problem is that the analogy doesn't even hold up in the source its referring to.

Sure, there are good player-coaches, but there are also great pure leaders. There are also very bad player-coaches. A coach who is trying too hard and too deep to be a player when they are less "fit" (or skilled) has historically led to many problems in many cases