...and none of them are in the SEC ...none are a state university either for that matter.
The IVY league invented football as we know it today . The competitions they had over 100 years ago thrust football into the mainstream . The forward pass was invented in 1876 in the Princeton vs Yale game. The ref tossed a coin to see if it was legal , and let it stand. He also invented the 'coin toss' as it is associated with the game. President Roosevelt later met with university officials and solidified the forward pass in the rule books because he liked it and it increased the safety of the game
All of the Ivy league schools used football to market themselves to student athletes and still do. They dont offer schollies like mainstream schools but use football to compete among themselves for student athlete.
Again , these teams are not in the SEC and they are not state institutions. Apples to Apples please. Football puts your school on TV and gives exposure to kids in other regions that never would even consider it. Further , at its highest level , it generates a cash flow for the academic side and the other non earning sports that they cannot get from the state or boosters . Also , you should really read up on the success stories of so many non-qualifiers that played college ball and went on to be very successful in the business world. How about the NFL guys too ? Is preparing a kid for a lucrative multi-million dollar job using one of the seven intelligences ( athletic ability ) not worthwhile?