I do not make decisions for other families but no one is an expert on everything and it is not just the socialization but seeing people from other backgrounds, cultures, religions, financial circumstances, that is part of school. You cannot recreate it other ways. Kids need teachers that are not their parents.
LOTS of public schools are not very diverse. There are schools that are all white, schools that are all black and schools that are all Hispanic. There are schools where all the kids are poor and getting free or subsidized lunches, and others where all the kids are well off and need no assistance. Some schools are diverse, but there are others that are not, so that is not always "part of school."
We have family that is on assistance, family that is wealthy and family that is somewhere in between; my extended family includes 3 different Hispanic surnames; our children have cousins of Asian decent on both sides; our children have two physically disabled cousins; our neighborhood is 50/50 black and white; our children attend extracurricular activities with children of all ethnicities. I wouldn't call that "recreating" anything. I don't even understand what you mean with that statement. How is my child experiencing diversity at school better than them experiencing it at activities and within their own family and neighborhood?