"However if I chose to educate my children independently , I am actively choosing to education in an environment that is not socially diverse."
not always.
we live in a naice, leafy green Surrey village.
there is a perfectly lovely state school at the end of our road. with an intake of nicely turned out, middle class, well-off children.
dd2 goes to the prep school at the other end of our road. with an equally middle class well off intake.
we chose one school over the other (for various reasons), but there is no difference in socioeconomic status between the schools (indeed 2/3 of the year at the state infant school are down for places at dd2's school for Yr3...).
to get social diversity of the type you want, we would have to go quite a way away for dd2's schooling.
ironically, dd1 is at a super-exclusive private school, and there is far more social diversity there. but it is a SN school, so dd2 cannot attend (it is also in the next county.)