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.

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.

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.