Is the socialization problem more due to lack of social interaction because they don't go to a school building, or more due to the kinds of people who homeschool being fringey types who wouldn't let their kids socialize with "normal" kids for fear of contamination?
Maybe I'm too "Midwestern" but my mental model of homeschooled kids is kids who were kept away from the sinful secular world by parents who really, really wanted them to grow up utterly immersed in one specific dogma, such that even the local parochial schools were too broad-minded for them. They're going to have problems integrating once they leave home, but it isn't because their parents lacked the opportunities to let them run around down at the local playground, and building more playgrounds isn't going to help them, because their parents wouldn't want them around "those" kids anyway.