A lot of issues require holding two ideas in your head at once. Age verification chips away at privacy and internet freedom. It likely also reduces harm to some/many/whatever children, even if it’s imperfect and won’t stop everyone. The interesting question is where the right trade off sits. People often end up arguing only one side.
Massively downplaying it to say "chips away" this takes a sledgehammer to the core of internet privacy. In all cases in the world where this has been done before like China or Russia, freedom is also lost shortly after. Of course people only argue one side, the stakes are losing internet privacy and freedom in the entire world if the west also succumbs to these authoritarian policies. It isn't the government's job to…
This may come as a shock but neither China or Russia had their first encounter with losses of individual freedom in the 1990s. This is what the OP is talking about, this is the kind of shibboleth of online libertarianism that has little to do with real world policy outcomes. You'll find many similar laws concerning child safety in Norway that you find in China, different political systems and cultures can value the same things, even implement similar laws, without converging on the same political system.
In most countries on earth protecting children is a collective job, not a parents private business. A functioning and safe social fabric is a condition for successful families.
Just worth mentioning one data point. In the US 50% of young men (aged 18-49) now participate in online betting or gambling, likely as a consequence of the saturation of ads on social media and gaming platforms. Good luck with your parental responsibility when an entire country operates like this.