What does a NFL coach do?

If you have HBO, check out an episode or two of the series Hard Knocks. It’s a documentary series that follows one team each year in depth, and you can get a sense for the many responsibilities of the HC.

There are also a few very good specials on Belicheck but he isn’t necessarily the typical HC, he does the GM work and is pretty hands on in all aspects of the team. Regardless it should give you an appreciation for how much work goes into running a team.

Can I cut in? :)

It's probably a misunderstanding to call them coaches. They're rarely coaching. At that level they are managers, with one foot in leader-ville.

That is, there is plenty to manage; plenty to lead. If you're coaching in the NFL then you're likely to be unemployed soon.

I'm not being snarky or troll-y. The assumption of the question is wrong.

Note: At the elite level of European futbol, they are properly called managers. For good reason. Words matter.

For one, they pick the offensive and defensive coordinators. I assume they set the tone for the offence and clubhouse, and keep things on track. I also assume that the two coordinators aren't equal as some head coaches emphasize one or the other and probably do it a bit themselves (such as Belichick).