alt Hacker NewsMost 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.
A lot of countries have limits on how long CCTV footage may be stored (often there is a minimum and maximum limit). I believe in the US it is regulated on a per state level.