This morning on NFL Radio, they talked about Dungy (and other HC's that didn't call plays), and highlighted how some HC's (like Tomlin) are 100% invested in the role while others are only 50% in because they are too busy calling plays. Tomlin currently has the Steelers at 6-2 and 1st in the AFCN with a QB duo of Fields and Wilson, and he has never had a losing season as HC of the Steelers, even with Kenny Pickett as his QB.
Payton seemed to have a rare ability to be both coordinator and HC, but the hosts complained that most play calling HC's are too lost in their play sheets to manage the team during the game. When things are going well it isn't noticed, but when things are going poorly then the ship just keeps drifting further into the storm with the captain nowhere in sight. That seems to be where we are now.