Hey man, there is nothing wrong with your logic. I agree. But that is not the NCAA model or objective. Typically, AD's are tasked with championships in each of the sports they are responsible for. To get and retain coaches for each sport at a top national university like UF they need to provide state of the art facilities.
I would be interested to see a breakdown of the percentage of dollars spent for football compared with the percentage allocated to all other sports over the past 30 years and what is the breakdown between booster dollars and gifts designated for specific sports facility?
An easier comparison is to look at the facilities at schools with no football program. I have two kids at Cal State Fullerton. CSUF is a huge state school (40,000+ students) located in the middle of Orange County, CA with over 3.5M people and just 45 minutes from the second largest city in the country.
They have no football program.
Here's some info on CSUF's facilities
Baseball Stadium capacity - 3,500
Basketball Gym capacity - 4,000 (yes, they call it a gym)
Softball stadium capacity - 1,000
Soccer stadium capacity - 10,000
CSUF is in the middle of fundraising to upgrade the Baseball and Softball facilities. They plan to spend $10M - $12M. The CSUF baseball program is a national power with 4 NCAA Championships and regularly competes in the college world series with their last appearance in 2017.
Amazing what programs at huge state schools in highly populated areas can thrive on from a facilities standpoint when there's no football money available.