I'll respond to your points if you do the same:
Cook by himself was not responsible to even close to 10-15 points of the deficit in the first half. Everyone struggled in the 1st half, and our defense was atrocious.
Why are you discounting his PER? Luka and Nick has higher PER's, but are you going to discount Joe's PER because it was 4th on the team? Is he not an important part of the team?
Put some of that aside, and just ask yourself what was Cook's role on this team. I would argue that his role was to attack and put pressure on the opposing team. Nobody on our team can get their shot like Cook can. Sometimes to open up the game, he has to force the issue, take the pressure and focus off others in order to free them up. When Tyler isn't attacking, we are a team that passes around the perimeter and settles for jump shots. When Tyler attacks the rim, it opens things up for everyone else on the team.
Is Cook perfect? No. Does Cook make stupid plays? Yes. Does Cook do things that nobody else on this team can do? Yes.
Now I tried to answer your questions, will you answer this question? Did Cook change the tenor and tone of the game vs Tennessee with his scoring the first 9 points of the 2nd half attacking Tennessee?