Overall a good philosophical discussion. It really boils down to this: does the SCHSL want to allow homeschool students to participate for SCHSL teams? If the answer is "yes" they can make it happen tomorrow by amending the SCHSL constitution (assuming there is no law that needs to be passed by the state legislature). Even if the answer is "yes" it does not prohibit a homeschool team from existing.
BTW, I don't think there is anyway a homeschool team could join the SCHSL or SCISA. They fundamentally deal education facilities that are brick and mortar.