The library is one place out of the many places you could go, and the closest digital equivalent is a library website or an app. The Internet is not just a library, but a whole world of its own. We don't have blanket control laws that restrict all movement and speech in the real world based on verified age. The restrictions for minors are implemented at much more local levels.

We do need parental guidance like in the physical world, but such guidance should be issued by the parents, not the tech companies. Age verification is about giving your age and some other identifying metadata to the tech companies, and they hold the authority to decide what to filter. It should be other way around. The companies should expose metadata about their service and the content in their feeds via public APIs, and let people filter stuff locally on the device per the device owners' aka the parents' preferences. Oh wait. Such features will never reach mass adoption in the current software ecosystem. Software antitrust is a joke. These companies and the feds have the opposite incentives and do everything to sabotage local solutions. They've locked down what OS you can run on the hardware you bought, what apps are approved on their walled garden OS, and only the official apps can access their APIs. You don't have root on your own phone and it's a brick without remote authentication. Now they can sell you parenting plus many other things as their exclusive cloud service because "the market failed to deliver" and you can't really control what software runs on your own phone, much less your child's phone. This is the upstream problem and we ought to see it clearly and assign the blame correctly rather than trust those who deliberately created the problem to solve it.