The reasons the Jets brought in Jason Taylor were simple. The team had nobody capable of consistently winning a one on one while pass rushing. The team could not generate pressure without blitzing. The team needed a guy who could get to the quarterback with the lead late in the game after a season in 2009 that saw the Jets lose several games in the final minutes.
I think by most accounts, Taylor failed to provide what the team was looking for. He had flashes, but he was inconsistent. The pass rush disappeared for long stretches. That is something of an indictment on the guy who was brought in to rush the passer. Taylor was to his credit very stout against the run, but the Jets had Bryan Thomas at the same position for that job. JT struggled in coverage, but that again was less relevant than his inconsistency as a pass rusher.
The idea was to limit Taylor's snaps to keep him fresh. I think this might have backfired. The games I remember where he played best (Baltimore, Miami, Buffalo to name a few) where ones in which he got a lot of playing time. Perhaps he is the kind of guy who needs to be in the flow of the game. In any event, the team still could not generate a consistent pass rush or get to the quarterback without blitzing with Taylor.