I really don't buy that the Longhorns killed the SWC. The SWC was rife with corruption, and they weren't even the worst! SMU actually killed the SWC, combined with the lawsuit NCAA VS Oklahoma University Board of Regents.
For those that don't know, OU VS NCAA is the law suit that allowed colleges or individual athletic associations negotiate new TV contracts. TV money became a real thing that didn't exist before (c1989). This killed the SWC, and drove the SEC to add Arkansas. Arkansas had to escape the insanely corrupt SWC which was completely dominated by the Texas state government. SMU's corruption was spearheaded by none other than the Gov of Texas!
Getting 12 teams allowed the SEC to form a championship game and sign a nice deal with CBS. Championship game==$$$$
The remaining members of the SWC did not think their TV ratings would be good enough and so worked with the Big 8 to form a 12 team conference (goal was a championship game) with otherwise not familiar schools.
That Lawsuit killed the SWC because the SWC had a bunch of forgettable teams (Cougars?, Rice?) that no one wanted to watch on TV.