I would similarly bet that people will readily exchange their purchase history for discounts/convenience. Even I find it convenient to not have to save every receipt for returning items and just be able to enter my phone number.
I just tell the cashier's I forgot my card. They just grab one off the stack and scan it.
This, of course, depends where you are. Randalls requires the card/phone number and the cashier won't even prompt you for it; you have to type in the number on the pinpad or hand them your card before paying.
I recently moved away from central TX where HEB is prevalent and that's one of the things I miss the most- they don't use any of this card nonsense and treat their employees well. Up here I'm stuck with Kroger and Walmart.
Of course, I'd prefer not to provide a phone number at all, but some of the local businesses (especially hair salons, for some reason) get downright hostile when I try to explain my preference. It's like it's completely unheard of to not hand your phone number out to strangers. This gives me a way to "relent" without causing a scene.
/me: "Abärr isch abäh gaa kainäh Ändieh!"
Also I see more and more shops which stopped asking. Finally.
mostly: Tegut, REWE, Lidl. Other than that: Bauhaus, IKEA, Bäckereien.
Though I changed my shopping to early morning, just before going to sleep, instead of "last minute shopping" before closing, after getting up late. So I'm a new face to most cashiers. Idea is less virus load after a night with no people and aircon having sucked it away. I'd hope. Can't say anything about IKEA or Bauhaus atm. Haven't been there for years. Didn't need to. Bakery? KNÄCKEBROT!
edit: But asking for some points collection scheme seems to be the default here, except for Aldi. And at least about half of the people do it.
I've noticed that this is mostly down to the cashier recognizing you and not some kind of policy change.
At my regular EDEKA some of the cashiers know me and know I don't do points collection, so they usually don't ask but sometimes still do just out of habit.
Cashiers that don't know me will still always ask.
Another EDEKA, where I only shop every couple of weeks and nobody recognizes me, I always get asked for the card.