Because we don't WANT them to have our kids all day. We don't want them to have that much input and influence. There's a big difference in participation in the school band and them being there ALL day.
I support the girl's desire to be in the band and I hope she gets in.
But your argument is a little specious. Your home-schooled kid can go to French class, because the teacher is really great, but not the history class, because it is being taught by a pro-Marxist deviant. My home-schooled kid should be able to attend advanced calculus class, but not the English class with all those politically-correct but mediocre authors. How on earth can any school district manage that?
I support home schooling for those who want to (we don't, although we have considered it). And I wish the home schooling parents would get at least some of their taxes back. But it is not about taxes, it's about the kids. You make a choice: your kid is in or out.