The digital world is not like the real one. When you show your ID once all it's details are saved and can be searched across. When showing your ID to the cigarette vendor they will not notice most data and will have forgotten it a while later. So we need to be more careful with the data we give out digitally.
No ID is needed, just proof that you are above a certain age. There are technological solutions to just give out that data, but politicians seem to not want to go that way. This is the real issue, not age checking. The fear that age-checking means tracking...