I certainly can't speak for every school, but at the major P4 programs football tends to fund the other sports. Meaning, it brings in more than it consumes. It's a net positive. While all of the other sports at most schools, are a net negative. They spend more than they bring in.
At some schools basketball is also a net contributor, and as you've pointed out at LSU (and also at Texas) baseball is a net contributor. But ALL those other programs, are detractors. They're a drain. And many of them will have to be cut, if and when schools begin paying football athletes as employees.
It's easy for every program to "run in the red" when there is no real business reason to turn a profit. All of these programs are government programs, even the football program. They are, after all, state entities and ultimately funded by the state (excluding private schools of course). Texas A&M football would not exist without Texas A&M University, nor would LSU Football or Texas Football. A lot of them probably run in the red because they're paying for new track facilities, swimming and diving, equestrian, and the like.
The only reason for the women's pole vaulting and equestrian (and many men's sports as well) is because Title IX forces the schools to have the same number of men's and women's athletes, and I think the same money spent as well. Not sure exactly how it works, but basically they try to even out men's vs women's, even though there is virtually zero interest in any women's sport at almost any school. Just like the WNBA, the sport is propped up by the sports that people care about, which is usually Football, men's basketball, and baseball in a very few cases. The rest are artificial.
Please don't take this that I'm in favor of shutting down women's sports in all sports. I'm not. I'm simply saying that many of these other programs are just very low interest and they would not exist on their own, or if they did they would be very low key.
I think softball would continue, track and field, and a few others like volleyball. But I think it would be a different version of itself, very regional, with minimal support.
