The point would be, to roll it all into the ID issuing process. I think most EU IDs already have cryptographic identities built in. The certificate issuing should probably be a state service as well. The alternative would probably be, just mail your birth certificate and a 3D scan of your anus to the private age verification provider of your choice.
It of course all falls back to a central state authority. But the process wouldn’t have to be more centralized and privacy-invasive than state IDs already are. Control of resident data could be kept at municipality level, and you wouldn’t need a central approver, that gets a running feed of all my age-restricted activities.
Before I sound like I’m soying over ID verification, I’ll add that all this junk can become insidious very quick, if it becomes easy to implement and gets used everywhere. I also detest beyond measure that my ID currently stores a scan of my fingerprint, and I hope the court-ordered deadline makes that shit illegal again in 2027.