I'm not sure it's that simple. This had multiple reasons spanning months/years. Very difficult to fire coaches like Les, Mack Brown, or Phil Fulmer.
I think it's a combination of many of those choices. Miles is certainly too stubborn. He did tie himself too much to JJ and then Harris. He also ruined Lee before all that. The game has passed him by as well. He also appeared to lose the culture here at LSU. Despite the kids still loving and believing in him there was no coaching up. No belief we will win this game. At the end of the day last year he should have been let go. I never believed this team was as great as the critics were saying. Not because of talent but because of Miles. That said, he did a lot of great things for LSU. I wish him nothing but the best. Now let's restore the greatness of LSU football!!!
I also forgot to mention Saban going to Bama is also a HUGE factor. Sure no one else is doing what Saban is, but Miles will always be compared to him and his program.
It is because he was stubborn that the game passed him by. Saban is not in love with Kiffens offense but he knows it is the next evolution of college football. Many coaches would love to just win with a Miles type offense because it is safe, but they know the outcome so they allow themselves to change. Les didn't do that. So those two options are kind of the same.