1. We definitely disagree here. The HC is certainly responsible for holding players accountable for actions that are detrimental to the team. I don't think there are many people who would agree with you on this point.
And yup- it's bonkers how much they (HC's) have to deal with, but this is why you hire good lieutenants to delegate and why they are paid millions.
2. Fungible? I'm not following your use of that word. Do you mean "dispensable"?
Regardless of your intention, I do agree with you here. The best HC's in my mind are essentially those that "do the least amount of damage". I highly encourage anyone to read this book about the Pats (BB, Brady, Kraft). You'll start to see some of BB's philosophies emerge. Basically, he admits he doesn't do anything special, but he avoids doing stupid things that sink his chances of winning.
It's just 1 portion of his responsibilities, but man we can talk about Tomlin's clock management gaffes for hours. This again points to his serious lack of event preparation...he admits in his pressers that he goes by his gut in terms of timeouts and philosophy. And with him doing the repeated errors in terms of clock management is an indication he hasn't learned from his incorrect choices. Is that a stupid thing that can sink your chance of winning? Sure is...especially at this level.
You can make the correct choice and still lose the game. You can make an incorrect choice and win the game. That's what I fear about Tomlin...he doesn't see the difference- only W's and L's and the results-oriented approach which is not repeatable. I mean ask any psychologist, statistician or any other subject matter expert in any field of your choosing: results are irrelevant, the process is most important.
There's a definite difference between not getting in your players' way to win the game and preparing them vs being extremely hands-off. MT has history and evidence that shows everyone he subscribes to the latter.