Completely unprovable. Lou could have hired other coaches too, the availability of Trotz was a gift by Leonsis. There are plenty of competent coaches that could have gotten them into the playoffs in that span.
We were a -1 in goal differential in the regular season in 2019-20. 7th place. Everyone in front of us was at least a +25 that year. 12 teams made the playoffs that year in each conference. We almost blew a 3-1 lead over Philadelphia, losing 2 OT games in Games 5/6. Game 6 was 2 OTs. That's nearly a full game of OT's in 5/6 where we couldn't score a goal.
In 2020-21, we had our best year, with a +28, but we somehow managed to lose Game 7 on a SHORT HAND GOAL. Yeesh.
In 2021-22 we finished UNDER .500 according to the snarks here who count the OT losses that way (37-35-10), or 37-45 according to the Zeekers of the world. Hardly a ringing endorsement of sainthood. We were a -6 in goal differential and finished 16 points out of the playoffs.
All this shows is what I've said many times here, you make the playoffs and take your chances on getting hot at the right time. That isn't coaching at that point, its players making plays at the right time.
My prime issue with the Trotz approach is that it was very taxing physically and mentally and it wears teams/players down. If you want to ask about getting to the ECF, here's an inconvenient fact to ponder; do we make it that far if those two years weren't shortened by Covid? 68 regular season games and 54 games in the 2 years. In the 2 full 82 game seasons, we won one playoff round and didn't make the playoffs. I don't think that is solely a coincidence.