That's a fair point.
My argument only applied to the age verification in the Danish app, which doesnt share the ID to any server.
The point is that you get a verification by logging in with another 2FA app, whos only job is to verify with the government server, that you are indeed a Danish citizen with official documentation.
Then the other app recieves that token that only contains an age group with a true flag. This token is then shared with the private companies.
As a stand alone solution to age verification that everyone needs to use, this is pretty well thought out.
If a Linux phone then comes around that everyone would buy, you could do it better, yes.