In fact, if these laws make the requisite infrastructure (ID cards that offer that functionality) a hard requirement then creating an anonymous web that nevertheless has age checks easier, not harder.
What you basically want is an ID card where you as the owner can decide what you want to share with the private business. And for age verification that’s basically just requirement fulfilled yes/no.
So if the law is well written then this could be an advantage, not a disadvantage. Preemptive cynicism isn’t helpful here.