You are certainly not alone in this line of thinking. The problem is, the misconception that brick and mortar schools have a monopoly on those aspects of education and socialization. It’s admittedly more work to find those environments, but in my experience, has been more than worth it.
My indoctrination comment was a bit tongue in cheek - while public school will offer exactly one version of how to understand the world, we have been quite intentional about teaching our children *how to learn* rather than attempting to sell them our worldview. This is discussed extensively in the episode and my book.