I do really wish we could play under one umbrella like UIL. All of our playoff systems would make so much more sense. And the playoff brackets could expand to what they need to be at.
So a little backstory to answer your questions. TAPPS is definitely the most played in the Private school System. But they do not allow Homeschool teams. This is kind of where the gap started to grow. Homeschool teams were once in TCAL, it was a big league back in the early 2010's giving TAPPS a run for it's money. Played State Games in the Cotton Bowl. But TCAL got very unorganized and "shady."
So a couple of coaches from San Antonio-Feast Homeschool decided to create a league of their own. For Homeschool teams and all alike in 2014.
This was the birth of TAIAO. The whole TCAL situation also had TAPPS create a rule where TAPPS Teams can not play TCAL schools.
TAIAO has expanded a lot though and takes in other private schools. Either schools that fall out/get kicked out of TAPPS or schools moving on from TCAL and TCAF.
TCAL now only has about 3 Teams. TCAF maybe has 6-8, but TCAF is strictly in the DFW area now.
I imagine a world where we could get everyone in one league and split everyone up into 4-5 team districts and do it true Round Robin style like UIL. But the main issue has been people bumping heads, and to many private schools doing "Shady" things.
Hopefully one day, we can figure it out. Instead of having 8 different "State Champs" every year.