The true rich will send their kids away to another state, or even another country, if that's what it takes to get their kids into a good school. To stop this and force all the rich kids into public schools you'd have to ban all private schools, not just in the state, not just in every state, but in every single country around the world.

The good news is the above doesn't matter, you don't need rich students to have a good school, you can let all super rich families send their brats to expat boarding schools in the UK and Japan without losing anything that matters to the rest. The entrance and attendance requirements that actually matter don't concern money, but rather student behavior and performance. It is possible to create great schools in poor communities with very little local funding IFF those schools are allowed to have strict requirements for behavior and performance and are empowered to kick out students that fall short of those requirements.