I agree,
SA is a lot smaller than people realize. Also not the wealthiest city.
San Antonio is the 31st largest TV market as assessed by Nielsen. This indirectly measures a combination metro size and economy. Not perfect, but I'm to lazy to look at Metropolitan statistical area and per capita income and such...
In looking st this only 4 cities below San Antonio has more than one Major professional team. With the exception of Milwaukee 3 have an NFL team and another. That makes some sense to me as NFL teams can clearly thrive in small markets due to their business model and people will travel a long distance to see the few games they have so they can operate based on regional appeal.
I suspect there is something to SAs proximity to Dallas and Houston that does lessen the chance.