In the lower classifications, I can see where the public schools may have been able to gripe a little.. but in 5A, the VAST majority of state championships over the past 25 years have been won by public schools (5 total, 4 by Evangel, and 1 by Rummel).
http://www.14-0productions.com/LHSAA_Class_5A.html
If the private schools leave the LHSAA and form their own association, what does that accomplish? At that point they are still split from the public schools.