The issue is the scale and centralization of information. Let's imagine that every bar has to not only check the id of every customer but do it automatically: every time you enter a bar anywhere in the country you must have your id scanned by a government-issued system. Are you still ok with it?

That's why we need privacy preserving designs.

But saying “we must abandon the idea of age verification in bar” is never going to work in any democratic setting.

Voters genuinely want to protect the children, without second thoughts.