It's a lovely theory, but it comes unstuck when you get to university entry.
Cambridge and, for all I know, Oxford, will sometimes interview a home-educated applicant if they can be persuaded that the applicant is up to scratch, but that is as rare as rocking-horse crap - and in the wider university marketplace the only place where I know that happens is with mature students, and they have to undertake at least a foundation course to prove they can hack a degree-level course.
Thus the home educated child is effectively disbarred from tertiary education.