I think what this conversation is in need of some perspective. Go look at what fans of other teams think of their coach. See what Preds fans think of Laviolette's love of Cody McLeod. See what Leafs fans think of Babcock's usage of Hainsey. Even on great, successful teams, the coach will often do things the fans don't like. In many of those cases it's because the fans are just wrong, like when they're mad a young player doesn't get minutes when in reality that player isn't good enough yet (usually defensively) to deserve more minutes. Sometimes the fans and the coach just have a different philosophy and value different things in players. And sometimes the coach actually is wrong. But the point is, I don't think Bednar does that much that's any worse than most of the rest of the coaches in the NHL. Maybe I'm wrong on that, but after the December this team had, it's a miracle that they're even sniffing the playoffs, and some of the credit for that has to go to Bednar.
Now, I'm not saying he's the best coach in the league or a genius or anything, but I've seen no evidence that he would be worse than any realistic replacement, and he has yet to have a genuine playoff calibre lineup to coach or an entire season of solid goaltending. If the lineup improves and the goaltending is solid yet the team still struggles to make the playoffs, then you talk about a coaching change. Otherwise you risk firing a good coach and replacing him with someone who might be worse.