Another thing to consider is the social aspect of your team. It is hard enough to build a team's cohesion when you are dealing with four different grade levels, but at least they have the common theme of what happened at school / teachers / etc.
Plus I do believe if you don't feel the public schools are good enough (or the right fit) for your child then you don't get to pick and choose the parts you want. Some kids only come to school for sports. They are motivated by the fact that if they want to play football, soccer, or whatever next season they have to apply them selves and pass x number of classes. Now what happens when Jeremiah comes in from his home school "class" and takes his spot? I know that the kid should just work harder to win that spot back, but it is like cutting to the front of the line.
I just don't see how it would be fair.