Kif, I'm not sure which area you are speaking about but I think your comments are a vast generalisation. My cd do not go to private school btw, but in our local area, all the private schools have loads of outside space and good playgrounds (our local Catholic private primary is on a 100 acre site with its own wood) whereas many of the state primaries have nowhere near that kind of space. DS2 goes to a 5-yr old primary which has a nice field and playground but the PTA had to pay for shading, a gazebo and games markings on the yard i.e. anything out of the ordinary was not funded.
The fact that parents choose to do a substantial commute to the school is not the fault of the school, is it? The school is located wherever it is, parents make the choice to travel there. Just because you go to a state school doesn't mean you get to walk there, as many people in towns and cities taking two buses to get to their state primary will testify!
I have no idea about school dinners in private primary but presumably the children have to eat something so they will be eating their packed lunches communally anyway, won't they? I don't think not having school dinners is a deal-breaker really, the take-up in our school is quote low, the majority of children take packed lunch. Does that make us deficient in some way?
Heavy homework is again up to the parents and children to manage, many people send their children to private school specifically because they think the day at state primary is not challenging enough for their child.
You come across as having a huge chip on your shoulder about private education tbh and some rather odd ideas about the set-up in most private primaries. Good luck to you if your dc attend a fab primary with good results, little homework, wonderful outside space and tasty school dinners, which you can walk to in the fresh air. Just be aware that is not the reality for many people!