Why would they? The only reasons to show ID I can think of is when watching porn or maybe when buying alcohol online, though I doubt stores will want to risk driving customers away with that.
Consider that stores create reward point systems specifically for the purpose of connecting a customer profile to purchases.
Or using social media, signing up for any account where you can post content, and soon creating an account on your own device.
As for why would they, the same reason there are hundreds of tracking cookies on every site.