If you go the coordinator route, then you can't do better than Elliott. Great offense and a great recruiter. It would definitely hurt Clemson and would also likely lock up Ty Simpson.
However, UT is in an obviously critical situation where this hire has to be the right one and they can't afford to take a chance. If they don't land a bigger name with a great resume as a head coach, then they are pretty much in the same spot they were in when they hired Pruitt...from a public perception standpoint. It wouldn't generate that excitement from those around the program or the fans. Like it or not, winning the PR battle is a big deal right now considering the public embarrassment of yet another failed coach and an NCAA black cloud. The hire of White was a massive PR win that let the college sports world know that Tennessee was done messing around. Follow that up with a big hire and the public perception of Tennessee's football program and its outlook are completely changed.
Alabama got a huge leg up in their rebuild due to the public perception of the direction of the program after hiring Saban. Suddenly almost every recruit was interested. Ok, so the Dodge Chargers didn't hurt...but every recruit saw an Alabama offer in a completely different way because that hire alone showed that they were going to do whatever it took to get back to the top.
He could very well be the right guy to turn things around, but Elliott wouldn't give the program that boost, and it's badly needed.