Many [teams] assign an assistant to be their conscientious clock manager.
Really? I've never heard this mentioned; all I hear are the complaints (generally justified) about a head coach's missteps. I'd be willing to cede that many teams follow this de jure, only to transition to the Cowher method in the heat of the game.
Regardless of the nature of the industrial organization of a football team, isn't it surprising that there are persistent errors with regards to clock management? How has this not been corrected?