> The problem is that any age verification system effectively becomes an identity verification system. And such tools rarely remain "just for kids"—they quickly become used for other purposes.

source?

No source but a possible counter-example: SIM card carries the date-of-birth of the user (because, really, part of the problem is that you cannot supervise what a kid does with their phone 24/7), age-restricted websites have a flag in their HTTP headers, browser get age from SIM card through the OS. Same goes with app stores etc.

Like copy-protection there's always a way to circumvent it, the name of the game is to make it difficult enough. And for parents, to make it very easy to set-up.

Source for this ever not being the case?

XKEYSCORE, the UK system brought in to allow warrantless surveillance for national security purposes and child abuse prevention, ended up being used for such minor offences as catching people dumping rubbish in other people's bin, or parents lying about their child's address to get into a better school district. In the United States, the same system was used for low-level offences like cannabis possession.