Maybe yall will disagree, but I don't think the HC should be doing tons on gameday. The HC selects coordinators and position coaches in the offseason. Its during that time the HC and GM and coordinators make their plans. The HC sets the vision for the coordinators to bring to life. During the offseason, when things don't look as they're supposed to, the HC does what he needs to correct things. During the early the part of the season, when things are still being worked out, on non-gamedays, the HC weighs in on the direction the team needs to go to improve.
With all that being said, on gameday, the HC needs to let his coordinators and position coaches do their job. If the HC were to start doing those jobs, then what was the point of filling those roles with other people in the first place? A football team is enormous and highly complex. That's why there are a lot of coaches to manage one.
On gameday, a HC needs to be assessing the game as a whole. Where are we on the scoreboard? Given how we're moving the ball, at what yard line and distance do 4th downs become viable? Based on how the defense is playing, is taking the punt most responsible? Do we take the FG? Can we trust the FG kicker? They also have to be a good manager of clock. That alone is something that can win and lose games. If the HC is doing everyone else's job, they're not doing their one. And obviously finally, performance challenges and generally dealing/manipulating the refs.
Ultimately, that's how I see it. I don't wanna see Harbs calling 4th down plays. That's Monkens job (although he's been shit at it). I want John to do his job and quite frankly he's not even that good at just those responsibilities. I don't think many would say he's a savvy time out, or challenge guy.