Here is just one solution that helps parents, and respects everyone's privacy: Zero knowledge proofs.
Which allow anyone who is verified by anyone already (i.e. credit card company, ...) to get a cryptographic key from that organization, that they can use to anonymously verifiably assert they are 18+ to sites, (1) without giving sites any other information, and (2) without their key source getting any information on what sites they visit.
> Is it a reasonable concern?
Yes.
> Parents are supposed to raise their children.
Yes.
Vapid questions and statements aside, ...
Here is just one solution that helps parents, and respects everyone's privacy: Zero knowledge proofs.
Which allow anyone who is verified by anyone already (i.e. credit card company, ...) to get a cryptographic key from that organization, that they can use to anonymously verifiably assert they are 18+ to sites, (1) without giving sites any other information, and (2) without their key source getting any information on what sites they visit.