As for higher science and math, it's important to point out that parents who aren't proficient can supplement such subjects with tutors or co-ops, entrance into the ps high schools, or community college classes.
You just haven't been creative enough or done enough research if you think homeschoolers are limited by being home even in athletics or higher math and science. This just isn't the case and the beauty of homeschooling is once high school years hit and a child shows an obvious talent or proficiency for something, they can devote more time and attention to it, actually making them the superior candidates in the long run. Just a few random thoughts;-)
Actually, I haven't done one whit of RESEARCH on this. Therefore, it all falls under the heading of my far-reaching, agile CREATIVITY of mind. (I speculated on this...LOL.)
Nonetheless, my frau is a high school teacher. I've watched the distance courses in higher subjects, and they simply don't work.
A co-op IS an institutional school. Why institutional schools were devised in the first place.
I've been a long-time fan of high school athletics. There is no community or pick-up league that even comes close to the competitive opportunities granted kids in the state high school athletic associations.
I'm not saying that local little league isn't a good thing, but baseball is far, far and away the best of the available athletic opportunities outside of highschool athletics. Nothing else compares to it. But it grows out of baseball having been our "national" sport for years with great interest at every level.
And if a homeschooler puts their kids in high school athletics, then they're turning again to institutional education. I don't mind that. I just think we should call it what it is.