I’ve got some bad news for all the school choice people. If you have intelligent kids who you care enough about to pay for them to go to a good private school, or live in an expensive area that has good public schools, you are not going to like school choice. The people you are paying to get away from are going to end up in your children’s schools and there will be no where left for you to go. It’s not going to work like people think it will.
It will still work if the private schools can expel students for behavior or academic issues. If they can not or will not do this you are correct and the "private" schools will turn into the same cesspits.