I'd don't have any particular love for public schools but k-12 is covered by government in the US. There's no reason that it couldn't or shouldn't extend down. In my view, education gets harder the older the students are. Regardless of how many years of school the public decides to fund, I think we should start as early as possible. There's a compounding effect to education; put in the time, effort, and money early and you make the future a lot easier.

Nothing can replace good parents but there's only so much that can be done to improve the general quality of parents. Given that society has a vested interest in the future of every child, I don't think it's unreasonable for government to try to do better. That doesn't necessarily mean the public school system; it could be vouchers, various incentives, etc. But just saying parents need to do it is a cop out, shortsighted, and unrealistic.