Butch beat Georgia and Florida in the same season, and still failed to win the SEC east. This is not the same. With the mass exodus to the portal, looming sanctions, and national view of our program right now, I think what you are proposing is optimistic, but unrealistic. Butch mismanaged a team loaded with talent. If not for Josh Dobbs, he would have been exposed much earlier.
There hasn't been a "mass exodus". Some good players have left. There is opportunity to gain good players this year and next.
When we know if or what the sanctions will be then that will possibly be a mitigating factor. But if it is in line with recent sanctions then it should not be the limit on improvement that you seem to think. You can miss a bowl and lose 2 or 3 scholarships for a couple of years and still improve.
The "national view"? What do you even mean? Do you mean your view? To most of the nation including those following CFB closely UT's NCAA situation is pretty ho-hum. It has happened to others. It will happen to others. UT is taking a few lumps like many do. On the field... I'm not sure how firing a coach that was a very poor HC for blatant NCAA violations has a harmful net effect on image. Do you seriously think keeping a coach who lost to Georgia State and a mediocre BYU team in one season then followed it up with a non-competitive 3-7 team the next... who paid players... would be better for program image?
Right now, UT has hired a coach that seems to have sterling integrity. They fired a coach who was crooked. Heupel needs to be more competitive than expected which shouldn't be difficult considering how low the bar is being set... and all those "image" things you are worried about go away.
The history of significant turnarounds over the last 20-30 years is that they happen quickly following a coaching change. Bama was a mess when Saban arrived. Players left. Others were shown the door. They played lots of young guys early. After one difficult season in which they were competitive in every game... they took off and started winning championships.
USCw had lost at least 5 games in each of the five seasons before Carroll took over. They were 6-6 in his first year and then won at least 10 games for the next 7 seasons while playing for NC's.
We don't have to see that yet. UT may not have enough raw talent to see that. But significant and IMMEDIATE improvement is NOT unreasonable.