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.
Focusing on the HSed kids who get into Ivy League schools or become surgeons, while laudable, is a slippery slope. What if most HSed kids became long-term unemployed? Would we say that HSing should be abolished? No way, because the right of a parent to have plenary control over their child's education is as fundamental as free speech, self-defense and is entwined with the right to self-determination. THAT is the basis for homeschooling.
Having said that, most HSed kids do very well academically and certainly better than had they been through the public and, I'd add, private schools. The reasons why are varied, but they emanate from love and sacrifice. Teachers on the payroll may be good, but they will rarely have the same level of concern as that of parents or guardians.
Regardless of academic outcomes, HSed kids simply think for themselves, and THAT is, inter alia, why they want to kill it.