Bertie, the idea you describe appeals to many parents. For some, it is somewhat successful and better than just school. But there are two big problems with it as it compares to full-time home education.
First, being made to do things at school seems to put many, perhaps even most, children off the whole idea. All day they are receiving unspoken messages at school, messages like these: "Learning isn't fun. If it were, you wouldn't have to be forced to do it." "Learning is too difficult for you to do without help from a trained teacher. You can't discover useful things for yourself." "You aren't competent to decide for yourself which subjects to study and how to do it." "Swots are uncool." It has a big impact. Many quite bright and curious children refuse to do anything at home that remotely resembles academics. They'll happily demonstrate their competence by learning everything there is to know about a video game or fashion, but if it's a subject which their teachers or parents want them to learn, they won't touch it with a bargepole.
Second, school just takes up too much time to allow children to follow their interests properly. On top of the 9-3, there is going to and from school, getting ready for school, and homework. If you love a subject, you want to immerse yourself in it, rather than being yanked away after an hour because you are supposed to be doing something else. An adult could be a leading mathematician in her spare time while also working a 40 hour week in a factory. But it doesn't happen very often.
Where does that leave you? If you don't believe in the value of school-based education then it is just the free childcare that you are wanting from the school system. If the price of that "free" childcare is higher than you want to pay, there are other childcare options if you are working or studying. They are pretty much all the same options you had when your children were preschool-aged, before the free childcare (school) was on offer. Home educating parents who work or study use a whole range of solutions to the childcare challenge.