While I think many overstate the importance of the coach on an in game basis like this, 4 minutes is huge. We saw last season how big an impact reducing Buff's minutes from 27 to 23 had on him - he looked way better with a bit less ice time. When you talk about 4 minutes of ice time, that's often most of what the 4th line gets, so it's nothing to scoff at.
You can say the defence is green and that's impacting results, and it probably is to a degree, but the D from January onwards last season wasn't green and they looked just as bad. The forward group is largely unchanged and they look the same, if not worse.
I think they just need a new message, a shakeup, and the coach is the best way to do that. No excuse for playing Scheifele and Wheeler 5 more minutes a night that your second line. I understand Scheifele might have had a bit more last night because they went down a C, but it's not that unusual for that to be the case.