If he wanted to get rid of Taylor just for the sake of getting rid of Taylor, he would have done a deal by now. He didn't go from no offers to a 2nd round + 6th rounder overnight. The Jags and Bucs were sniffing around him too before the draft. There was an article quoting several anonymous NFL G.M's who said they would give up a 4th rounder for him. He could have released Taylor if he really wanted him gone that bad. He just stood firm on what he thought Taylor's value was and refused to trade him for less.
I agree that Parcells wants to change the culture of losing and selfishness there, but part of establishing an attidude of change is letting the players know they can't just publicly mope and whine their way out of their contracts or off the team unless it's good for the franchise. Just like when Ellis was trying to whine and cry his way off the team and out of his contract, the Cowboys stood firm and called his bluff and eventually Eliis had to tuck his Eeyore tail between his Eeyore legs and mope his Eeyore butt back to camp. It sends a message to the players that we'll trade you if we get a trade that's good for us, but we're not going to let you as the player dictate the situation to us when you're the one under contract.