As a competitor at a public school, I'm not sure I would like having seperation between public and private. Sure, I would have a better chance at placing, but I wouldn't really be swimming against the best of the best. I believe that it is unfair that private schools have so much more of an advantage in regards to facilities, coaches, training, and athletes (oh, what money can do) but it would be kind of depressing to compete at a public level and always know there's one step above me.
What would be a cool possibility would be a public school championship (say, Division II) and a private school championship (say, Division I). Each championship could have time standards that competitors would have to meet so they could advance to a state championship. To make it fair, maybe Division I could have harder qualifying times to balance distribution from both Divisions. That way, at the final state championship, everyone would indeed be swimming against the best of the best.
That's just my take on it though. I'm just happy to swim.