While the LHN rubbed a lot of folk the wrong way, remember the history. Texas tried to get the rest of the Big 12 to form a conference TV network like the SEC has and already had at the time. The Pac-10 had one too. Despite Texas supposedly running the Big 12, it couldn't get everyone in line to do that. Then Texas asked OU to partner with it on a network, but they dithered. Texas gave up and got its own, then others in the Big 12 were jealous and it rubbed them the wrong way. Despite mostly broadcasting Texas baseball, girl's softball, girl's volleyball, tennis, golf, men's and women's basketball and replaying old games. I don't see Texas in the wrong there.
Texas just isn't going to have the votes to seek to diminish Vanderbilt's share. But I do agree somewhat. I don't think either Texas or OU are going to have some of the same attitudes you prize. Texas fans won't chant SEC, SEC, SEC after hearing an announcement of some other SEC team's win (unless done ironically to mock the Aggies). In personality, we won't be much like Texas A&M that has embraced SEC as its mantra and a part of its ego. But don't think it will just be Texas, OU will have the same attitude and maybe more so.
But I am not sure Georgia, Florida and LSU are quite as unselfish as you might fool yourself to think. Otherwise wouldn't Florida not seek to block Florida State from the SEC and Georgia not block Georgia Tech? Even on these boards isn't the discussion of Clemson to the SEC about how it would be bad for SC? I haven't seen a single poster here say: "I know it would be bad for SC, but it would be good for the conference, so we should be unselfish and promote Clemson to the SEC."