State schools run special interest programs for some sports. e.g., Blackwood for netball, Brighton and Heathfield for volleyball, Ascot Park for gymnastics. I'm sure that happens in other States and Territories as well. Kids apply and can try out to get into those special interest programs, which means those schools end up with lots of kids who end up in State and National teams for those sports. In a sense this is a case of private schools doing a similar thing.
The only time I'm aware of a school having some form of limitation placed on its participation in a national schools' event is a high school in Canberra, which happens to be the school where AIS volleyball scholarship holders go, because it's close to the Institute. Until a couple of years ago, they had a limit on how many AIS kids could play in their team at the Australian Schools Volleyball Cup. The others had to play for their "home" school. In the last couple of years, they've been allowed to play anyone in their Open team, which has seen them playing more AIS kids and making the finals in that group. However, I believe they are ineligible for points towards the overall chamion school. Not sure about that.
As long as the private schools also place an emphasis on academic performance, then I doubt there's much to be worried about. It sound very much like the special interest schools' model that I referred to above, which I think has been accepted pretty well in the public systems.