I think part time schools should exist. So your child could go, say, Monday Tuesday Wednesday, or Thursday Friday Saturday. Two classes could then use the same classroom.
Or how about having my dream educational situation. A learning centre, with a library and resources for casual use, and regular classes. So, key stage one (or year one, or even level one) maths is on a Tuesday and Wednesday morning. If you want to be part of that class you register at the beginning of the year or term, then you come every Tuesday and Wednesday morning. You might be in level one maths, but then come for the level 3 science on a Wednesday afternoon. Then there could be special events - eg Thursday could be the "specials" day, when there is a timetable of different things that happen - there might be a show, or a huge craft project, and again, you put your name down at the beginning of term.
In the learning centre, there would be the option to book your child in for supervision with a vague age group, in a similar way to a private nursery. So you might need your child looking after from 3-5pm, and they could go there for more than looking after - there would be qualified people who could help them with any projects or direct play etc. Maybe a teacher overseeing, with TAs and even some of the teenagers helping out, but on a very casual way - there would be no lesson plans, so it would be more like a homework club, where the children could either follow a passion or work through their homework from either their parents or the classes.
You would be able to book one on one time with a teacher, TA, specialist or, again, an older child who had volunteered, for special help or advice on specific things, or just a bit of a chat around a subject.
There could be more obscure classes too - on a Monday from 3-5 it might be Latin, or The History of Football, or whatever had enough interest. The centre could be used for adult classes in the evenings, a mixture of OU type stuff, basic skills and hobby type things.
Sigh. It sounds complex, but with even just as many children as in one mid size primary school and a small high school, it would work. Not as a solution to everything, but one in each town or so.
I think it would make learning back into a whole life thing, rather than the chore than lots of people seem to think it is.