I hate this analogy because it isn't true. This isn't like a clerk checking your age before you buy booze this is like a clerk taking a photocopy of your ID and a list of everything you bought and then storing those records forever every time you buy alcohol.
they literally do that though. They don't all just look at your ID any more, some scan it with a scanner or phone and that literally does what you just said. Paying with a card also does it.
Most stores already have continuously-recording CCTV, which effectively does that too.
At least online there can be a separation between the age verification provider and the online content provider, so that the latter doesn't learn anything from the former except that the user's age is above or below a specific cut-off point. So it can actually be more privacy-preserving than purchasing age-restricted goods over the counter.