I think your comments are helpful. But I wanted to remark on this one:
the thing I regret most from my homeschooling experience is that I never had the opporunity to play a sport seriously.
Our kids are still young, but they have always played in little league sports, and I know many other homeschoolers who also put their children into little league.
But, in our experience, coaches do not teach "teamwork" like we expected, and most don't even teach how to play the sport. Things get competitive by age 6 or 7, and kids with natural ability or those whose parents can afford sports camps excel, while the others are pushed aside at a very early age. There are plenty of politics at play in little league, and even some public-school parents I know won't put their children into sports for that reason.
If anything, I think we put our kids into a bad situation by putting them into sports. It could be just our league - not very good role models there. Now I just want our children to be with other homeschoolers.
Anyway, so that's what you missed by not playing sports.
It is for the reasons you describe that my parents chose not to put me into little league. I did learn to play tennis pretty well (mostly playing with my brother, who didn't play on any teams either), and in my case I was referring particularly to was the fact that I never got the chance to play this in high school. There are usually a few sporting options available to homeschoolers, but as you describe, sometimes these are sub-optimal.