For those who successfully "enrich the education of their children, what makes you believe that couldn't be done by simply supplementing existing public resources?
Now, my children are reasonably successful, not overly, but reasonably, and the public resources in our modest town far exceed the enrichment my children availed themselves of.
So in reality, I don't get the need for homeschooling. If you want to enrich, supplement. If you're doing for political/moral reasons, my experience is that those kids end up weird and don't often excel academically. And as Mike has pointed out, show me any studies suggesting homeschooled kids excel above the norm athletically.
Perhaps the only time I can see it being sensible would involve certain types of disabilities, where the care is so specialized, maybe only a highly equipped parent can do it.