So is K-12 education, yet, this country managed to provide that, for decades, free, to the end user.

Sure. But K-12 education is inarguably necessary, and is commonly provided (for free) by virtually every country on earth.

Child care, though, tends not to be - for the simple reason that there is almost always an alternative to having the child(ren) in a child care center. Care at home.

In some states, the annual cost of infant child care is about $20K per year. In that scenario wouldn't make sense for the state to pay that amount to pay a third party to care for an infant so that the parent could work, unless the parent is working for more than $20K per year. You could instead just give money to the parent instead, and let them stay home.

Child care isn't necessary for the child's development (unlike K-12 education) - it's necessary if the parent is going to be able to leave the child to go to work. Since child care is very expensive relative to other employment, and is only going to get more expensive relative to other employment over time, it is a really thorny question whether free child care is a societally beneficial practice compared to alternatives. Unlike K-12 education, which clearly is. Which is why almost no countries provide free child care for infants or very young children (<3 years old), and none of the four countries that do offer full time free child care:

unicef.org - UNICEF Where Do Rich Countries Stand on Childcare

That's the reason why, unlike universal free public K-12 education, even the most generous rich countries don't have similar programs for early childhood childcare.