Ironically, the data points in the exact opposite direction. Homeschool students perform better in almost every metric compared to public schools.

>replace formal education with the nonsense that is homeschool.

I don't count public school as a formal education. I think of it as a daycare subsidy to make more parents work.

My daughter (16) is homeschooled and volunteers at a local private school where she teaches English and Code (in Scratch). I volunteered at the same school last year. It's given me a real insight into how important parent involvement is in education, regardless of what method you choose.