I think I was unclear, or you're rounding my view off to a very different one that I admit is common.
I'm a child of teachers, and I know quite a lot of people who teach in inner cities or narrowly made it out of impoverished towns because of good education. There's a reason I said "as well as an educational system", and I definitely don't believe the daycare role of schools is a reason to cut budgets or cut schooling.
Educating kids is hard. Many people lack the time, knowledge, and resources to substantially educate their children themselves. Many students benefit from years of often-repetitive teaching to ensure information is available when they're developmentally and environmentally ready for it. I don't doubt any of this, and I absolutely think public schooling is a sensible solution to it.
My point was only that "you could say K-12 education acts as a state sponsored vacation" misunderstands the role of schools as daycares. Non-educational time at school isn't a vacation, it's a public service for two-income households that struggle to afford daycare. I'm not talking about teaching kids math. I'm talking about the existence of three-recesses-per-day kindergarten, or middle schoolers sitting in voluntary, teacher-run study hall after school.
The district I grew up in had a public debate about whether to move to half-day kindergarten, where the two sides were "it'll cut school costs" and "it'll cost parents more in daycare". No one even claimed it was an educational debate, because less than half the day was spent on education. None of this has anything to do with whether teaching literacy in the Bronx is important.
I'm simply asserting that "provides childcare for free" is an intentional benefit, not an accidental drawback, of public schooling.