The other thing OP presents is very different from any eID scheme in terms of anonymity. You'd show an ID to a human at the counter and even if the seller stores your info somehow, it can't be linked to the token they sold to you. The required infrastructure is minimal and relatively simplistic. The only drawback is that being anonymous means it's easy to resell tokens.

An eID system links your real life identity to any use of the eID online. Anyone who thinks there's a math or technology that fixes this misses the fact that it's the trust in the humans (companies, institutions, governments) who operate these systems is misplaced. Math and technology are implemented by people so there are many opportunities to abuse these systems. And once in place I guarantee, without any shadow of doubt that sooner or later, fast or slow, it will be expanded to any online action.

I will take anonymity and the small minority of kids who will find a loophole to access some adult-only stuff over the inevitable overreach and abuse against the large majority of people whose every online move will be traced and logged.