Babcock is far from being the problem, the guy had been given a mediocre roster at best and yet coached them into the plaoffs 2 season in a row. I think the reception around the league is "very hard but fair" and that's exactly what you want from your coach. A coach isn't someone who can/should let his personal feelings disrupt his ability to ice the best roster he can with the given material.
Babcock got a bunch of superstars to play a team first game for him and absolutely crushed the olympics. Guy is by far the best coach in hockey and there is a reason why a guy like Super Mario is only offering a one year coaching contract (2 year payment).. Once Babcock is gone, people will start to realize how fortunate he were with him.