Meanwhile, the Rangers immediately went to the Finals once he was gone and no longer holding back offense, and the Conference Finals after, and did so with a terrible coach. In his one year with Vancouver, they missed the playoffs for the first time in 5 years and made it back the second he was gone.
Unfortunately, the facts contradict your story:
ES scoring
2009-10: 2.38 (19) PP 6.82 (12)
2010-11: 2.41 (18) PP 5.88 (19) 1st rd
2011-12: 2.49 (10) PP 5.69 (23) CF
2013: 2.40 (15) PP 5.54 (33) 2nd rd
2013-14: 2.25 (19) PP 6.48 (15) SC Final
2014-15: 2.86 (2) PP 5.91 (21) CF
2015-16: 2.68 (3) PP 6.71 (20) 1st rd
2016-17: 2.81 (5) PP 7.11 (12) 2nd rd
So the more AV opened up the offense, the worse the Rangers became.
When they sent to the SC Final, Rangers average 1.92 goals per game ES,
What got them there was Lundqvist and his .927 SV%
Cooper got the Tampa Bay job because he was their AHL coach the years before that & had a lot of success. He was coaching guys like Palat, Johnson, etc. in the minors before him & they ultimately got promoted to the NHL with Tampa.
It’s not like he just jumped into a spot after being somewhere else. He was there in their system at the minor league level cutting his teeth while their next wave of impact players were too.
Same with Sullivan in Pittsburgh.
Still "right place at the right time."