Liquidated damages being included in the contract is not for Butch to just sit at home and get paid; there's a reason there are stipulations attached to the payment of those damages.
an obligation to use your reasonable best efforts to mitigate the University's obligation to pay liquidated damages by making reasonable and diligent efforts as soon as practicable following termination to obtain another comparable employment or paid services position.
'Choosing' to spend 2+ years as an "analyst" at Alabama in spite of being offered coaching positions that would fulfill the "comparable employment or paid services position" would nullify UT's legal obligation to pay out liquidated damages to the extent that they are doing so at this point. Again, that clause isn't about making Butch take a job that he does not want to take, that's always his choice, but the university is not obligated to continue to pay him liquidated damages if he is not "making reasonable and diligent efforts as soon as practicable following termination". Two full years after termination without obtaining a coaching position is not reasonable or diligent by any stretch of the words.
Even Dooley went out and got a job with Dallas after he was fired, and his buyout from UT was guaranteed regardless of whether or not he found another position; Butch's is not. He has a legal obligation to seek out and find a comparable position. After two years, UT should make Butch prove that he is doing so, if he is unhirable, then Butch and Jimmy Sexton need to go on record saying as much. I have a feeling that if this scenario ever were to come to pass, Butch would have a coaching job 48 hours later even if it were Division II.