They were dominated in the playoffs under Lavi (2011-12, check the advanced metrics, terrible, just got lucky that MAF melted down in the first round), Berube and Hak. When this happened under three different coaches in four playoff appearances, uh, maybe the problem is more than coaching?
And you can't just change coaches,
St Louis, 5-5-1 under Berube
Chicago, 4-12-3 under Colliton
Kings, 7-12-1 under Desjardins
It's working in Edmonton, but that's the exception.
Coaching changes midstream:
CBJ 2015-16, Richards started 0-7-0, Tortorella 34-33-8
Pens, 2015-16, Johnston 15-10-3, Sullivan 33-16-5 [with major roster changes]
NYI, 2016-17, Capuano 17-17-8, Weight 24-12-4 [100 points the previous year]
NJD, 2014-15, DeBoer 12-17-7, Bench 20-19-7
TB, 2012-13, Boucher 13-18-1, Cooper 5-8-3
Toronto 2014-15, Carlyle 21-16-3, Horachek 9-28-5
Buf, 2012-13, Ruff 6-10-1, Rolston 15-11-5
Buf, 2013-14, Rolston 4-15-1, Nolan 17-36-9
Bos, 2016-17, Julien 26-23-6, Cassidy 18-8-1
Mon, 2016-17, Therrien 31-19-8, Julien 16-7-1
Ottawa, 2014-15, MacLean 11-11-5, Cameron 32-15-8
Fla, 2016-17, Gallant 11-9-1, Rowe 24-27-10
Win, 2013-14, Noel 19-23-5, Maurice 18-12-5
Minn, 2015-16, Yeo 23-22-10, Torchetti 15-11-1
Stl 2016-17, Hitchcock 24-21-5, Yeo 22-8-2 [107 points the previous year]
Edm 2014-15, Eakins 7-19-5, Nelson 17-25-9
Kings 2011-12, Murray 13-12-4, Stevens 2-2, Sutter 25-13-11
Good teams often rebound for two reasons:
1) regression to the mean, a good team on a slow start simply plays up to its talent
2) tuned out the old coach who overstayed his welcome, See Boston/Montreal in 2016-17
Bad teams often fail to rebound, because, well, they were bad.
It also helps to identify the replacement coach before you make the move, that is, either a veteran coach or someone in your organization, instead of a stopgap interim coach out of desperation.
The biggest danger is the interim coach gets a bounceback, you give him a long-term contract, and find out why he was available: Yeo in St Louis, Rolston in Buffalo, Weight with the Islanders