so sure, each case is different, and you are not wrong, but you are putting to much value on good institutions. the heavy lifting still comes from the parents. your children are doing well because you care that they do.
But, that was part of my point above. My sister to this day feels like she never had the supportive and attentive relationship with our late mother that she needed. (For what it's worth, I agree with her.) In my imaginary reality, at least, if she'd been the only child at home for a few days a week, while I was at day-care and then school, maybe she'd have grown up feeling differently.
I see good parenting and good institutions - that's schools, but also parks and pools and little leagues and libraries, and, hell, even good policing - as mutually supportive. It's unfair to expect one side of the individual / community matrix to make up for all of the shortcomings of the other, but each can strengthen the other side.
Admittedly, my wife and I are fortunate to be able to pay for him to go to an excellent pre-school (though the one local to my parents was similarly good), and I see him naturally acquiring a social fluency and confidence with his peers that I didn't have (if I even do!) until I was an adult. Furthermore, had I been cared for outside the home, my mum would have spent vastly more time with my sister when she was an infant and toddler, which I think would have been a lifelong benefit to her. I also think my mum would have been personally better off getting back to full-time work ~5 years earlier than she did: full-time parenting wore on her, and she and my dad would have been able to retire a few years sooner.
Those are all highly-dependent personal circumstances, so I'm not going to draw a universal rule - but I'm telling you this in order to caution you against doing the same. All families, and all individual circumstances, are different.
[Second thought] I am going to make one general point: the benefit my son draws is highly dependent upon attending a good school. Institutions absolutely exist where "dumping them" is an appropriate epithet to apply, but there is no reason why that has to be the case. I don't know where you live, but in my country the "pro-natalist" political party is also devoted to policies which make schools worse (cutting funding, lowering teacher pay, meddling with curricula, etc), which seems to me to be perverse.