My parochial school was poor working class. I learned how to talk crassly, 'shoot the shit', be prematurely sexual, to accept fate, etc. I did not learn how to speak properly, be diplomatic, set goals for life, better myself. Those I learned in college when I went to school with much better off kids and realized that all these things were things I could deliberately aim for and accomplish.
So, while attending school gave me a leg up in understanding the typical American 'everyman' (a skill which is severely lacking in silicon valley and in 'elite' circles in society), it did absolutely nothing to help me achieve becoming part of that elite. In many ways it hindered me. It taught me a worldview where everyone was coming to get me, to put me in my place, etc.
It's age-segregated, usually monitored by adults, extremely regimented, and often very hostile.
There are a million different contexts where kids can learn better, more useful social skills, like at church events, youth athletics, with kids in the neighborhood, etc.