I can't say I'm a fan of this, but I'm trying to stay open-minded. I also realize there's some really lousy public schools. But there are also some excellent ones in some jurisdictions. I'm in one, and am adjacent to several more.
My fear would be during the kid's H.S. age, because I can't imagine any parent that would be able to give their kid a truly excellent competitive education in full breadth, at least compared to the better schools I'm familiar with. I just can't imagine most parents able to do well in things like Calculus, Physics, Creative Writing, Chem, Bio, Debate, etc. I can see a parent having superior skills in one or two disciplines, but not across them all. And that's to say nothing of extra-curricular stuff like music, sports, etc.
Colour me skeptical. I can see a kid getting a basic moderate lower level education this way, but I have my doubts of then being academically prepared to get into higher-level competitive schools. I'd be worried I'd be knee-capping my kid, not allowing them to realize their full potential & breadth.