First challenge is avoiding the distractions. There are a wide range of these. A gamut of social duties totally unrelated to coaching football, representing the university in all kinds of venues. Having to interact with the media on an almost daily basis. Having to interact with boosters and state politicians on a regular basis. Having to manage the business side of the program, from budget to hiring, firing and the day-to-day staff problems, to driving key decisions on facilities and grounds. And then, the fame, the distractions of the other sort, the kind that let you blow off steam (but could land you in trouble if you go too far in any of a variety of directions). Just a world of distraction beyond what Coordinators feel. Can be easy to lose focus on football. This seems to be what got Sarkisian. It was Butch's biggest weakness. And Dooley's. And Kiffin's. It's definitely what got guys like Price at Bama a decade or so ago.
Second challenge is the expansion, almost explosion, of leadership span of control. A coordinator may (or may not) have leadership responsibilities over the position coaches on his side of the line of scrimmage, but every head coach has responsibility for the selection, guidance, mentoring, and leadership of every single assistant coach, plus a fair few other key members of the extended staff. If you just want to design plays and teach players how to execute them well, this can be a super hard part of the new job. Blemishes in his leadership style may be what got Taggart.
Third challenge is delegation. As in, learning how to. Because he's now responsible for both sides of the ball, and special teams to boot, the head coach must delegate some of what he was used to doing (and not only doing, but doing SO WELL that it's how he got the head coaching gig!). It's hard to let a subordinate take over one's specialty so that he can devote more attention to the other aspects of the job. But gotta be done. This may have been Smart's challenge. Frankly, this is the one i thought might get Pruitt, but he seems to be doing a good job of delegating as much as he needs to (while still staying pretty strongly engaged in the defense during most practice periods).
There are certainly other challenges as well. Those are the big three, as I understand the job. And I listed them in the order that they probably hurt careers. Distractions most often, then leadership stumbles, and finally inability to delegate and get the wider view.
Thank goodness we seem (so far) to be beyond all three with CJP.
Go Vols!