I do not think parents are the one pushing these controls. They are busy raising the kids.
There’s an alternate view that parents are very much in support of centralized policy. When policy is left up to individual families — little Johnny X has an iPhone but little Timmy Y doesn’t — the creep towards everyone having a phone begins. When, instead, the school board bans phones it’s much easier for the conservative majority of parents to hold the line.
I think parents are raising the alarm about nefarious social media practices (ie recommendation algorithms that actively do harm) and those services are in turn pushing these controls in order to deflect responsibility away from themselves.