One can cherry pick examples of coaching changes where programs improved in two, three, four, five, six, seven, eight and any number of years. There have been enough examples over the 125 of post-Camp college football there you can find pretty much an example to use as "support" for any argument.
What we know if the the metric for Charlie Strong staying at Texas was the team show "improvement." If you want to call running your feature back 52 times and losing against Kansas "improvement," you certainly convince yourself a game like that is indicative of a team that is playing better and better on a consistent basis.
But using Charlie Strong's record as support for an argument that he should be retained because he is about to do the same thing at Texas is absurd. It is about as valid as saying LSU should hire Les Miles as their coach because he has shown he can win a national championship at LSU. He won one in his third year at LSU, so we should expect him to win a national championship in his third year wherever he is hired (including back at LSU) because if it happened once, it will happen time and time again.
It doesn't work that way. Nothing Charlie Strong did at Louisville should be a factor in deciding whether to fire him or not. The two situations are totally disconnected.
My personal opinion is that Charlie's personality fit well with the mid-major status of Louisville where the media and booster demands were less than at UT. He is somewhat introverted and not suited well to the booster and media demands at Texas. he would MUCH rather be in the coaches offices than dealing with other program demands. At Louisville, he had the time to spend with the players and assistant coaches and wasn't as dependent on his coordinators to entirely run their side of the ball. I don't think Charlie has spent the time in Texas to understand who the young position coaches who also have strong recruiting relationships are and, as a result, he listens to the advice of others and makes mistakes like hiring Jennings. Charlie isn't good at evaluating coordinators.
Charlie has some big time weaknesses that make him a poor fit at a program like Texas. Charlie will never be the right coach for Texas, regardless of what he did in his third or fourth year at Louisville.