You think UT football is more important than it actually is as compared to running the state university's $2.3 billion budget. Athletics is part of Statewide, Student Services which is only 7% of the total budget.
So UTK Athletics Department including the football program is the larger fraction of the statewide STUDENT SERVICES budget category of which athletics is a sub-category and football is a sub-sub-category.
Granted, the UTK AD is self supporting, but it's a little more than peanuts compared to the whole.
Now, having said that, as Dr. Andy Holt, the president from 59 to 70 and oversaw UTs largest growth, observed that, "Football is UT's front porch". And it does have serious economic impact on Knoxville and Volunteer football's reputation impacts many things across the state.
The bolded part is key. The University System has a $2.3 billion budget. Large, to be sure. But isn't a lot of it, from year to year, kind of on autopilot? How much do the allocations to various things really change each year? Is there even a lot of serious, required debate about it each year?
What Holt understood (accurately) is that athletics, particularly football, has a great impact on the reputation and brand of the entire university system. It's hard to put an exact dollar value on that, but it is immense. It affects the perception of the university not just in the state but nationwide. And that's not even talking about the economic impact on Knoxville and the surrounding area. I was in Boston last summer and one of the days I was there I wore a Tennessee polo. I was walking down the street and a Boston cop, stopped in his patrol car at an intersection, started singing Rocky Top. That's purely because of football. Now, does a person in Boston knowing the Power T and Rocky Top bring in another dime to the school? No, but I think you get the point.
The impact that the success of the Alabama football program has had on that school and the entire state is immeasurable and will last for generations. Hell, Bear Bryant is still very much the "brand" of the University of Alabama and he's been dead 35 years. Saban has even furthered that tradition and their national brand. Enrollment at UA, particularly out-of-state enrollment, has exploded there over the last decade (hundreds of millions more into the coffers). The overall impact of their football program alone, over the years, is in the billions of dollars. Both for the University and Tuscaloosa/Birmingham/the surrounding area.
Rightly or wrongly, football has outsized importance here and at many other schools. But even when appropriately sized, it is still very important. So yes, I absolutely think Davenport could be fired for a football-related decision.