Let me spell this out, not necessarily for you, but for those who share your opinion. We have two entities. There is the Vol football team, and then there is Derek Dooley, who has the good fortune of being the Vols current HC. Derek Dooley is not the team, he is merely a coach, and coaches can be replaced.
Now, we as fans, who recognize Dooley's limitations and know our football team deserves better, have only one way to speak to the AD that he will listen to. He does not care about angry emails, he wouldn't care if we picketed his office, what he does care about is money. The only thing he will listen to is his wallet when finances start going south.
Does that mean we're not supporting the team? No. I will still root for the team to win, but I will not give my money to Hart so he can continue to employ a subpar coach. We are supporting the team by telling the AD these young men deserve a coach that can lead them to victory. They deserve a coach who can develop their talent and help them reach that next level. Dooley is not that man.
Going back to your first paragraph, you say you don't give a $h!t who coaches the Vols. As a fan, shouldn't you care whether these young men are getting the coaching they deserve? You say "real fans" are the ones who stick around during times like these. Who's left? We're all here passionately making our case for change. Not going to a game doesn't mean we won't watch them on TV and cheer for them to win. It's not my place to say who is or is not a "true fan", a term thrown around way too often, but it seems to me a fan wants what is best for his/her team. The fact you think Dooley should go at all says you do not believe him to be what is best for this team. So why accept it? Why not demand change in the only way the AD will listen. If revenues drop, Hart will know fans mean business when they say it's time for Dooley to go. If he wants our money, he needs to earn it, not give it away to a subpar coach.
If Hart cannot figure this out, then the next AD will.