This is a bit of a false dichotomy. Wealthy people can send their kids to good public/private schools because they can afford to live places with access. But less-wealthy people may not have the option.
The social interaction piece is interesting, and may be addressed by the fact that there is massive growth in homeschooling right now. It's also easier to connect/coordinate with other families (remote or local, based on interests/age). Not a bad idea for a startup, actually!