Asking for Rutgers finishing ranked multiple times in 11 years while in the Big East seems a little like asking too much for me. That's like asking UConn to finish ranked multiple times in 11 years. The fact he finished in the top 15 one year, while winning at least 8 games in 4 of his last 5 years (while at Rutgers) is proof enough to me that he's a great head coach. I could see him not working out at Tennessee because he's a Northerner trying to fit in with Southern culture and how the SEC works, but not because he isn't a good head coach
You and I have very different definitions of "a great head coach".
Even if you're generous and don't count his first 2 years (due to taking over a dumpster fire) at Rutgers which were his worst years, his winning percentage is still just 58%...playing in the Big East. At that time it was with Pitt, UConn, Louisville, WVU, Syracuse. Miami, VA Tech, and BC left in 2004...and miraculously, Schiano's actually started to have winning seasons. Even then he went 7-5, 11-2, 8-5, 8-5, 9-4, 4-8, 9-4. Even if you only consider his Big East record, his best finish was tied for 2nd twice (2008 and 2006), keep in mind, Miami and VA Tech already left by then. Otherwise, he finished 7th in 2003, 6th 2004, 3rd 2005, 5th in 2007, 4th in 2009, 8th in 2010, and 4th in 2011. 2011 being his last year at Rutgers. None of that says "great head coach" to me. It says he was an OK coach.
Louisville (under Petrino and Strong), WVU were able to make multiple appearances in the top 25 during those years...why couldn't Schiano at Rutgers do it?
Also, as a college head coach, the off the field responsibilities and fit are just as important than the on the field stuff. Moreso in college than any other level because of how the HC has act as a fundraising figure with donors. You can't separate that from a HC's duties. Even CPJ, who is notoriously *****ly in front of the media, is actually quite personable with donors and fans when he's with them.
EDIT:
Also this to consider: At Rutgers, football isn't the 247-365 obsession it is in the SEC and especially at a school like UT. Schiano could do things with relative anonymity compared to the microscope he'll be put under at UT. You think someone like Schiano would hold up well in that environment when he also has to coach against coaches like Saban, Malzahn, Smart, Mullen, an improving and recruiting ace like Orgeron, Smart, and whoever TX AM gets?