As someone stated earlier, the AISA already exists, but competition in it is voluntary. Frankly, it's almost unfair to the private schools who choose to play in AISA to wedge schools like St. Pauls and Briarwood into that universe. Those schools play in that league because they know that they don't have the horses to compete with other schools in the AHSAA, mostly the public schools. Sure, they might be afraid of someone like St. Paul's, but again, that's not who or what they're principally trying to avoid. Frankly, for most of those schools, sports is a secondary concern anyway.
Speaking for my school, we also choose to play in AHSAA rather than AISA, but the desire to play better competition has little to do with it. Frankly, the most significant concern is the travel expenses. While requiring all private schools to play in AISA would make the field larger, it wouldn't change the fact that, in order to play a full schedule, we would still have to travel hours and hours away for many of our road games due to the lack of private schools in our geographic area that play the major sports. That's not an issue for public schools that are districted with schools of equitable classification and geographic proximity (and are funded by the government/taxpayers), but it's a huge deal for small schools with tiny athletic budgets and a primary focus on education that would be jeopardized by sports teams having to miss copious amounts of school due to travel logistics.
As for the thought that schools like St. Paul's and Briarwood are pillaging the talent of the local public schools, perhaps it is happening. Again, so what?! What are you going to do? Restrict scholarships? What about private school scholarships that go to the underserved or are classified for the arts? Those kids could play sports, too, or are you going to say that if you receive financial aid that you shouldn't be eligible? That's not just wrong, it's reprehensible and un-American. The answer for the AHSAA was to create a rule that penalizes ALL private schools due to a short period of sustained success for a handful of those institutions. Like that's fair. [/sarcasm] Here's the answer: organize your efforts, start early, get better, and beat them. Or better yet, wait for the inevitable downturn that happens to every school due to the generational ebb and flow of talent.
What I can speak to is the idea that those same schools are "cooking the books" in order to keep enrollment at a certain level in order to maintain a certain sports classification. Seriously? Unless those schools are literally Scrooge McDuck swimming in cash, no private school is turning away full-paying students. To think such is a fallacy of logic and belies a fundamental understanding of supply and demand in the private sector of education.
Again, this entire discussion is being driven by the reactions of a couple of people to the actions of a handful of schools (and the state's ill-advised attempts to try and placate those who see success by private institutions as unfair). If I want to live under a system that punishes individual success and de-incentivizes efforts to create, innovate, and win (whether one thinks the means to get there as legitimate or not), I'll move to a country that embraces socialism or communism.