It's not a question of whether or not coaches have an influence or make a difference, it's the question of what exactly their role is or should be.
I think most fans and even clubs buy into the ridiculous fact that the coach is the one most accountable, and even if the clubs don't believe that, they usually save face by changing coaches.
In a healthy organisation a coach can step out of the system without too much disturbance. There are good examples of this in other sports, Luke Walton with The Golden State Warriors, being one.
Does anyone here really think Bellamy leaving for a couple weeks would suddenly result in Melbourne losing or dismantling into some sort of Warriors type mess? (Of course long term absence is different - take Des Hasler for example, he's there, but not there.) Even with the absence of players like Cooper Cronk for example doesn't automatically mean the team will collapse. So Brodie Croft comes in and kills it.... just proves the point that their organisation is doing the right thing.
The sooner people stop buying into this myth and individual responsibility means fair accountability then you'll have greater club success, otherwise you'll just have more of the same - high coach turn over, constant player transfer, shorter contracts etc....