He hadn't fallen off a cliff as much as he never had that much of a chance this season... 165 off and on plate appearances is not enough to judge whether or not a player has fallen off a cliff.
I think the toxic clubhouse is media nonsense, I don't believe there is too much too that.
If the Red Sox had kept Youk in the lineup, do you honestly believe the record would be much better? I don't... I think they would be about .500, maybe better if Youk picked it up. Not having Youk or Middlebooks for that Yankees series really hurt the team. Middlebrooks has missed a bunch of time since the deal, and Youk has played everyday and played well. (not saying he would have here, but it is a possibility.)
So the last thing I will say about this is that had the Red Sox given Youk another full time chance, they would probably be in a similar position and they might be able to have dealt him for a better package.
Just my opinion... it's impossible to say what would have happened, but to discount this possibility is foolish.