This would work if you assume that there is minimal value in the accumulated knowledge and cultural artifacts of generations, and that every child is able to rediscover/re-invent calculus, classical physics, the alphabetic system, formal writing conventions, etc. on their own. Possibly if your first name is Leonardo, or your last name is Leibnitz.
I think child-inspired learning makes more sense, as in, using their interests as starting points that lead into areas of knowledge that they might not have chosen on their own, but for which they have a better sense of the relevance, when connected to their interests and ambitions.
Besides, if you're homeschooling, getting through a core curriculum in under three hours a day would not be unusual, which leaves plenty of time for child-led exploration anyway.
I've also noticed, more cynically, that most of the families I know who claim to unschool have weeks that are just as overscheduled as the prep school families. They just spend a lot more time driving around to different specialized classes and tutors, instead of dropping them off at the one-stop private school.
