You're mostly right that it's not about child safety, but in that case why are you asking for suggestions about how to do it? What goals should age verification have if child safety is not accepted as a goal?

Parental control already exists, but seemingly valid criticisms are that it is not a default, has limited effectiveness, and is not easy enough to use. The important detail here is that there are not widely accepted standards for it to interface with online platforms, which are now being pressured to develop privacy invasive child protection schemes they implement independently. What I'm suggesting is that instead of that, letting them rely on "verification" of whether a user is on a restricted device would do mostly the same thing in terms of benefits and be less harmful, if more work is put into building a standard for that and making it an easy to use default.