Some people follow a curriculum, even the National Curriculum (though I've never met one of those IRL). The big advantage this is perceived to have over school by those who advocate it is exactly wht you describe - efficiency and the possibility of really getting your teeth into something which is of particular interest (and there may well be other factors ruling out school, like religious beliefs or bullying or some sort of SEN which the System hasn't dealt with or all sorts of other things).
Then there's the kind of "strewing" model, where a parent has in mind what they want their child to learn, and they leave relevant things lying around hoping the child will get interested.
And that segues, I think without much outward difference but a shift in parental motivation, into an autonomous model, where the parents provide all sorts of resources and follow the interests of the child. That child might spend a whole year ostensibly studying nothing but football, but when you unpick it, there are all sorts of literacy and numeracy things going on, all sorts of opportunities for art and sport and lord knows what else.
being interupted - sorry this is only half finished...