In many ways, you hit it on the head.
Many people point to the test scores and other quantitative measures of homeschooling excellence, as a quasi-justification for homeschooling. These are good points to have. But...that utilitarian argument is a lot like resting the right to Keep and Bear Arms on John Lott, Jr and other researchers' quantifying the benefits of firearms ownership.
In both cases, the individuals' right to KABA and the parent's right to homeschool does not hinge on a cost/benefit analyses, nor is it subject to legal debate. They simply ARE.
I know of homeschooled children that won't become rocket scientists, or may be of average intelligence. But these kids know right from wrong, and can withstand 4 years of college indoctrination and come out as stronger Americans.
What IS of inestimable value in homeschooling, is the love and care and support from the parents (or guardians). Many homeschooling families aren't one-percenters and they may not have parents/guardians that are upper bell-curve inhabitants. But we will fight to the death to ensure our children aren't chewed up by the system, that they get as good an education as they can deliver, and (on some level) NEVER stop the dedication to our kids.
Not to mention that parents can pool their expertise and act as teachers for a pod of kids.
In some states you don't even have to be certified in a subject to teach it...in a public school.
As I was reading your post, I was thinking of one of my kids. My wife is decent with math but nowhere near his level. His math skills are extremely good and he sailed through college.
He actually is a homeschooled rocket scientist, well Astronautical Engineer to be precise. With a nice career path at NASA.
But, we let our kids follow their own path. His younger brother is a Trucker. He doesn’t earn as much but he’s mature and independent. He has the most important job in the family. He drives a flatbed semi. Not only is r=he expected to drive safely, he’s solely responsible for his load to be balanced and secured. The lumber he delivers to construction sites keeps hundreds of men employed and able to feed their families.