IMO it is best to keep kids as far away from entitled rich kids as possible which probably means keeping them away from private schools. If that means packing lunches, so be it.

The education in both public and private schools is so garbage, I would also rather kids be in public school since it will be way easier to get good grades and take up less of their time, as the purpose is mostly just social.

Any real education will happen at home for kids with STEM employed parents.