As mentioned earlier, you can’t look at this with football blinders on.That post answered your question. Now you move the goal posts by changing the question. After you get rid of the privates how do you get rid of LWE, MS, ESL, Rochester, etc. Because 99% of the public still won't win a title?
FWIW, In 1A the 4 finalists in Boys soccer were private schools and in Volleyball, 3 of the 4 finalists are private schools. In soccer, they all came from areas where the public schools play 3A in soccer and at least 6A in football. The smaller privates pull from a larger pool of athletes in towns of 25,000+ in population yet compete against schools pulling from towns of less than 5,000.
The size of the school may not matter but the population density sure does. Not sure how you solve the problem. Maybe you make classes based on the population of the towns schools, both public and private, are pulling from.