I think one huge advantage of homeschooling is that you can tailor the curriculum to the interests of the child: when you are in the school system you often are boring a child because out of 30 children at least some are going to be bored by a topic or have already learned a topic. You can avoid that in homeschooling.

I do think though, obviously, as you mentioned, that homeschooling is wonderful for special needs children. You didn't mention but homeschooling is also great for gifted children who are easily bored by public school. My brother and I are both gifted and were bored through all of our schooling, both private and public, until I hit grad school, where I finally met others who were really enjoying the learning process as well. I think schooling is kind of aimed towards teaching that theoretical "average" child of which there really are so few. Most children, really, may have some deficits and/or gifted areas and so really will benefit from homeschooling in my opinion.

Of course, the reality is not every parent may have the personality, desire, financial situation, or willingness to homeschool so homeschool may not be an option for that reason. And then public and private schools are other options to be considered in that case.