It didn't work when they lasted one more playoff series in 11-12. They got handled by the Devils with a roster that actually played together and showed up for games, even the non-star players.
The difference is changing/swapping huge, important chunks of your lineup yearly and losing character guys like Fedotenko, Prospal, and Prust. Guys like that created the identity the Rangers had for those 1-2 years, not so much Tortorella. Tortorella just turned the team (arguably unnecessarily) into shot-blockers, but those players gave the Rangers an identity of a hard-nosed, no BS, tough to play against team.
This season, no one was firing on any cylinders in the regular or post-season except Stepan, Hank, and McDonagh. That's another difference between seasons: Last season, everyone was trying and it was visible, even if they weren't producing. Guys were getting bounces because they were engaged. This year, there was none of that, no hustle or "jam", at any point and it was noticeable. When your captain is invisible for 95% of the season, things probably aren't going to turn out well.