I don't think kids should get to choose. Some parents are too busy to teach kids, and some kids wouldn't take lessons from their parents seriously. Kids may slack off and that would affect their career eventually.
If, in any way possible, you could get a tutor to work for free several days a week, several hours per day. Still, the kids might slack off and not take the tutor seriously. A school environment is good for kids because they have other children there to help them and support them.
If the government could somehow provide a tutor, like if the parents are busy, the tutor can do it, and if the kids are slacking off, then they can't choose to be home schooled, they would automatically have to start going to school again!