Easy, you take control of the rep teams, and insist that to be eligible you have to play for your local club.
Watch the kids gravitate to where the prized selections are available.
When the school threatens to drop club players to 3's, they won't care & the power is then transferred.
Short-sighted to try to "remove" schools, who do actually provide resources, from the process. The private school system is flawed, but marginalising it does not seem to me to be the answer. Kids at schools don't have the time to serve 2 masters, so to speak. It is quite reasonable for schools to want them to play sports for the school. I think the answer lies in more inclusive comps rather than the ridiculously small comps we see in Sydney, for example. The GPS / CAS mentality is increasingly flawed. Get them competing with Independent / Public schools. And club teams. I know it won't happen but they need to get them out of these bubbles. But don't deny the schools have an important role to play.