I'm not so sure Texas would still be the helmet school, because from about 1940-1970's they were pretty much the only flagship school in the state. In the 60's A&M was basically equivalent to what the Citadel is today. A small military feeder college that didn't admit women (IDK if the Citadel admits women now). A&M was winning championships from the inception of the SWC all the way up to WWII, and in fact won the 2nd MNC (AP Poll) in 1939 just before WWII for the United States. Coincidentally TCU won the first.
The War changed the CFB landscape, Army scooped up most of the best recruits, and A&M was hardly ever the same. After the war most students and recruits wanted to forget war and all the things that go along with being in something like the Corps of Cadets.
In the 50's we got kinda close with an all-time coach (Bear Bryant) but mamma called and we were a non-factor until the 70's. In the 80's and 90's we won 9/10 from UT and a bunch of SWC championships.
Given that we went from about 6K students in the early 70's to 70,000 students now do you think Texas would have the same huge head-start? Hell, even with all those things working against us we're still a top 20 all time program, and I could easily see us sliding down to the low teens a-la LSU or Florida.