You're still thinking it at a the level of "can", rather than the level of "is it worth it".

"Possible" isn't the same as "profitable" - the whole point of stores doing it would be to sell that data to entities such as Health Insurers, and that data would be sold at pennies (and I don't mean pennie-per-entry, I mean pennies-per-thousands), so it has to be possible to do it extremely cheaply, which it is if you already have the necessary information in digital form in a database (user id from the payment card and the list of items purchased along with date, time and location of purchase), but it's not if you have to do reverse image search in bulk, not least because the providers out there won't just allow other businesses to do it for free to make money out of it - they'll demand a cut for doing the computationally hardest part of the process (or, if the supermarkets want to do it themselves, for access to their store of pictures).

Also, the quality of results from reverse image search is pretty bad in terms of actually finding and correctly identifying a person from a picture - it often just outright fails or gives false positives, which means data obtained that way is a lot more polluted with false results than just finding the person ID via the card used for payment, which is near perfect (not quite perfect because somebody might let somebody else use their card or the card might have been stolen, but way more reliable than identifying somebody via a picture).

So all this hassle and cost to have a parallel process to try to ID people like me who pays in cash to sell my purchasing habits information, when most people are like you and just give them their ID on a platter by paying with card, doesn't make any business sense.

They ain't doing it because they can't, they ain't doing it because so long as the market is flooded with customer purchasing habits data obtained cheaply by just using the information from their card payment, deploying facial recognition technology to match buyers to purchases wouldn't actually be profitable.

Just because it's technologically possible to go after the hard to get info using a complex process, doesn't mean it makes business sense to do it, especially when they're already making money with a far simpler and cheaper process.