@peemee Yes. For a time then my key ring had like 15 of the little buggers - libraries, grocery stores, hardware stores, pharmacies, …. And they get torn up and rubbed off not infrequently. (Some newer ones have fixed this, luckily.)
Now I mostly rely on the different stores being able to look up the membership by phone number or member number, and I don’t carry the cards at all.
But I’ve never seen a small door card. They’re always large and slightly thick IME. Probably to protect the electronics.
/@jextxadore