Yes, Offensive Coordinator Lane Kiffin should have been retained because he was a successful coach. At the college level, a person should rise and fall based on their success. It should matter if the person is liked or a good person. Instead, Kiffin should have stayed because he was a winning coach.
Leaving Alabama one week before a championship game was certain to cause speculation and drama that most teams try to avoid so close to a title game, and Kiffin's duties with Florida Atlantic were negatively affecting his performance at Alabama, but it would have made more sense to keep him on through the bowl season and then let him pursue his coaching job elsewhere. His departure was inevitable, but the timing is certainly curious.
He probably had a great deal to do with the success that the Alabama team has experienced, but he knows that. He can have a much better job, being head coach, somewhere else. I don't think there was much the folks at Alabama could have done to keep him. Who wouldn't trade in an assistant position for a head coaching job?
Football coaches have one job to do. They need to do everything they can to make sure that their team will win as many games as possible. Alabama has not done well so far this season. Lane Kiffin's poor performance was a big part of that. He deserved to be sacked.