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Even when there isn't, you'd still have private schools which are fully tax funded. Private schools can choose who is allowed to attend and every family can choose which school to send their kids too, it's not restricted to district.

Maybe not in the UK, they're a bit special, but for the rest of Europe this approach is more common. Now since there isn't much regulation on what defies a private school as for size, you can basically start one that serves only your local neighborhood or street, such small scale school would essentially be like home schooling, assuming you can trust your neighbors.

Better yet, there's a lot of freedom on what to teach the kids, and how you'll do it. You wanna teach them actual useful skills, and use more practical learning then go ahead. Those methods are proven to work and many private schools does exactly that.