Homeschooling and private schools are huge around here.
One family moved to a big city for the dad's job, and with all other struggles (mom had surgery, other stuff) they decided to place their always homeschooled 15 year old in a very good private school because they did not have time to "plug into" all the homeschool offerings.(see below) She tested well, has friends galore, is in the school play and active in church, and the hardest part has been following a regular schedule.
One teacher, upon meeting her, said, "oh, you have always been homeschooled, I see. I do not expect you to do very well in my class." Well, she exempted her final and he basically has since apologized for his incorrect assumption. She received academic honors first semester!
As for what to do if parents are bad at math, setting up labs, running phys ed, etc...
there are SO many places that cater to homeschoolers that you'd be amazed! Academies that run one or two days a week, entire sports teams at gymnastics centers and swim centers, churches that host open classrooms, field trip days at local historical and fun places, open houses for book and curriculum sales, support groups, even legal defense for tricky states! On-line courses, tutoring, skype lessons, study groups, etc...
in fact, some colleges recruit homeschoolers because they know they will not have to necessarily train them how to study and set aside time to study.
yes, there are always a few bad apples (a HS girl in her 3rd year of basic algebra) but you have bad apples anywhere you go, public, private, homeschool, boarding school, etc...
A big part of it is motivation. that "unschooled" boy is unmotivated because he gets what he wants--free play time! The poster above who explained how it should be done was spot on.
That comes down to a parenting issue.
We all have our own opinions. if we all thought the same, we would only have one clothing store, one church, one restaurant, one type of car, etc...there is no "one size fits all." But we can all mostly recognize a good thing done well.
And there are many good homeschooled kids.