To think that LSU had interest in these sports due to the success of the other instate schools is ludicrous. Not taking away from the other schools or putting LSU on a pedestal-but the cause and effect is not there. Like every other SEC/BCS school LSU competes and tries to build programs in all of these sports, and pretty much followed the same timing of development in these sports as other similar schools. Might have developed some sooner or later in some sports than some of its peers. Generally smaller schools got into baseball, women's basketball and softball sooner, the Southern football schools didn't get as much into basketball as they did football until later. You could apply your theory in a lot of other states-but its more the pattern of development of the sports-not an LSU-other Louisiana school thing.
I don't know the academic side as well-but if your rationale is as strong, well ...