First, the way we’ve been taught stall recover for a long time has been focused on limiting altitude loss above all else. This works fine in small trainers. In larger planes, the very first thing you do is get the nose down. You need to restore flow over the wing, so you need airspeed. Airspeed ultimately is what recovers from a stall, not power, not nose position, speed.
So you punch the throttles, and you lower the nose, both of which give you speed. Then once you are no longer stalling, you start to reduce vertical speed while maintaining that airspeed. As margins improve, you continue to raise the nose into a climb, and fully recover.
The Colgan air crash had a second more dangerous component though. It was an asymmetrical stall. This resulted in one wing dropping in the stall. If you try to fix that with ailerons, as is natural, you’ll actually deepen the asymmetry as well as deepen the stall itself. As a result, it becomes even harder to recover.
Yes it could be saved, but every action taken as the plane approached, then entered the stall, was wrong and each one made recovery less likely than the previous one.