That's not true. Trotz had a single year where the Islanders were solidly in the playoffs, his first. Every other year they were battling for a wildcard spot.
--Capuano Era--
2012-13, 8th place.
2013-14, 14th place.
2014-15, 3rd place in the division, 3 points above the last playoff spot.
2015-16, 7th place.
2016-17, 9th place.
--Dead Weight Era--
2017-18, 11th place.
--Trotz Era--
2018-19, 2nd place in the division, just 5 points above the last playoff spot.
2019-20, 7th in the conference on win percentage.
2020-21, 4th place in their division (the last playoff spot).
2021-22, 9th place.
--Lambert Era--
2022-23 they're currently in 9th, a single point outside the last playoff spot.
The results have been the same for a long time during the regular season, even with Trotz. This has always been a bubble playoff team. The difference is that when they got into the playoffs with Trotz they had success, because his system is tailored for the playoffs. Lamoriello is also a defense first guy and fans hate it, even when he tries to get a bit more offense.