The main reason it "isn't practical" is that many states only allow children to be homeschooled by their own parents (or a licensed teacher hired by the parents). As a few people on this thread noted, group homeschooling would be a great option for families that can't afford, or just don't want to have one parent completely leave the workforce. One parent could afford to stay home and teach, if she was getting paid a few thousand a year by parents of a few other children she taught along with her own. This would also allow for some grouping of kids by age, ability level, or special needs.
Of course, teachers' unions fight tooth and nail against proposals to allow non-parental, non-licensed teacher homeschooling, and other nanny-staters at the state level enact laws tightly regulating in-home child care in a way that would classify most group homeschoolers as in home child care businesses, and which would in many cases seriously interfere with running a homeschool the way you want to (including a good deal of remodelling of your house, visits by inspectors to make sure you don't have anything accessible to children that hasn't been government-certified as lead-free, fenced yard (even if you're on a remote dirt road), etc.
From time to time, I've perused the HSLDA website and been disturbed to note that this issue doesn't seem to be on their radar screen at all. I'm sure it would easily triple the number of US children who are homeschooled, if all states were pressured into allowing group/non-parental homeschooling with the same minimal restrictions that many already apply to parental homeschooling.
tutoring is illegal? Home piano courses?
Yep, and yet in several states that do not allow group homeschooling don’t require all teachers to be “certified” teachers in public schools, but require private schools and group centers to meet those requirements. That REALLY PI$$E$ me off!