I’m not sure I get the arguments based around better education quality. One of the primary controllable determinants of a child’s educational attainments is parental involvement. Spend a couple of hours with the kid going over their homework and helping them stay a chapter ahead, and I bet the kid would not only be academically successful but also socialized.
Also, a lot of school systems have a fast track learning program for gifted students. You might have to shop around for a school with one if you’re in a low population area, but I think that driving your kid for 45m to a STEM high school probably takes less time than lesson prep and teaching.