Well, and that service then inevitably being hacked and your ID being distributed and/or sold to miscreants online.

I'm in the UK, I'm normally connected through a VPN these days.

It’s possible to build mechanisms for this. Not perfect or foolproof ones. Maybe your phone stores a digital ID for its owner and sets a cryptographically signed “IsAdult” header. If you pull the signing key from the phone you can spoof that, but you can bring a fake ID to the bar too.

The problem is that the people who want age verification don’t really care about the technical details of how it’s implemented and the people who oppose age verification just want unfettered online pornography out of principle, so no one is actually thinking about how to implement age verification in a way that protects privacy.