I do think the playoff success is a straw in Rex's hat moreso than Sanchez. I don't accept those WC/Divisional round games as reasons why Sanchez will come out of it.
They were supposed to be one of the reasons Sanchez would become good. Playoff experience/wins. He has not become good. Making it far in a team game is not attributable to Sanchez.
Use your eyes, Sanchez is bad.
With Rex, it's harder to tell because he doesn't "perform" anything, but going on track record...if he has a team with good talent, he can be successful. Playoff appearances are more attributable to the coach than any one player, since he coaches the entirety of the operation.
The main thing I don't like about Rex is the team will come out with a weird defeatist or 'we can't hang' attitude. That may be a trickle down effect of having Sanchez though. It's probably hard for the players to be inspired to go out and play against Tom Brady or Ben Roethlisberger and the 6 ring Steelers when they know their guy is Sanchez. You saw it Sunday, they replaced him, the line went nuts and blew Arizona's d-line off the ball, Greene was crashing through guys and even bouncing off.
Rex thought (like most Jets fans) that Sanchez would be good. He thought that the departures of the entire offense besides Mangold, Moore, Brick and Keller would be okay because he knows QBs can compensate. He was wrong about his.
Unfortunately Rex has been handicapped by Tannenbaum and Woody. Rex has also made some shit decisions in drafting and during the various free agency periods. That's why he needs a real GM. I hope he gets a chance here.