“However, I think even places where kindergarten isn’t mandatory, the attitude communicated to parents is “you have to put them in kindergarten or they’ll be behind”. I bet the same happens with preschool once we start paying for it.”
I’m sure you’re right..
And, the kids who “need” Pre-school, can likely already get it through Head Start or Special Ed.
I think one of the reasons for "universal" preschool is that middle class parents don't want underprivileged children getting either government paid day care or a possible educational edge on their own children - so to an extent that is true already.
I've seen some studies suggesting that Head Start doesn't work as well as was hoped in part because they hire uneducated, low-income parents as caregivers and in part because there is not a rigorous or set curriculum to provide remediation to these children.