This is a debate that seems more or less settled on the Rangers board lately. Yes, he does keep on making mistakes and the Rangers have the power to get rid of them when they turn bad.
After 2004, there was a youth movement on the team. It took a long time to coalesce because it was happening while the team was legitimately competitive. Take a look at the 2004 roster, pre-firesale, and you will find Brian Leetch, Alex Kovalev, Jan Hlavac, Jed Ortmeyer and Jamie Lundmark as the only "homegrown" players to play more than 50 games. Leetch was drafted almost 2 decades earlier and Kovalev/Hlavac spent significant time elsewhere before rejoining the Rangers in 2003. Ortmeyer and Lundmark the only 2 under 25 on the roster, not just homegrown. In 2005-06, you had Henrik Lundqvist, Ryan Hollweg, Petr Prucha, Fedor Tyutin, Jed Ortmeyer, and Dominic Moore. Plus Marcel Hossa and Blair Betts being 25 and under and getting their first real shots at regular NHL play. Granted that the general quality of the youth wasn't particularly high. Lundqvist and Tyutin were the only ones to have solid careers as better than 4th line/3rd pair/backup G players.
That kind of thing was the usual case during the Jagr era. If you skip forward to Jagr's last year on the team. 25-and-under, over 50 games: Marc Staal, Brandon Dubinsky, Nigel Dawes, Ryan Callahan, Dan Girardi, Petr Prucha, Fedor Tyutin, Colton Orr, Ryan Hollweg, and Henrik Lundqvist. Orr was the only non-homegrown player there.
It continues and when you skip on to the year the Rangers finished first in the East, the story remains the same, although some of the homegrown guys are a little older then. 25 and under: Del Zotto, Stepan, McDonagh, Hagelin, Anisimov, Stralman, Dubinsky (Staal played 46 games). Homegrown over 25: Callahan, Girardi, Lundqvist.
And finally, last year when they went to the SCF. 25 and under: J. Moore, Kreider, Stepan, McDonagh, Hagelin, Brassard, Dorsett (plus Del Zotto, who played the first half of the year with the team). Homegrown over 25: Staal, Zuccarello, Girardi, and Lundqvist (plus, the return of Dominic Moore, Callahan was part of the team until the deadline).
There's a hugely noticeable difference in the way the team is run as far as internal player development since 2004. A lot of people credit the salary cap for that and I think there is some truth. On the other hand, when the Rangers had their firesale in 2004, Sather had convinced ownership that the team needed to go through a rebuild. The team leading into training camp in 2004-05 was absolutely horrendous on paper. There's a pretty good chance that, if there had been a season, Sidney Crosby could have easily ended up a Ranger. As it was, 05-06 was a bit of a surprise. The emergence of Hank and the resurgence of Jagr meant the team was competitive when they weren't planning to be. It changed Sather's entire 5-year plan.