This is incredibly wasteful. Back when I had a Kroger I would just play dumb and ask for the discount, even if I get a new card each time, because I refuse to carry their card. Not wanting to hold up their line, cashiers would either scan their own card or scan a new card and give it with a blank application, which I'd promptly trash. For those unfamiliar, they have laughably high prices on a lot of common items, unless you have your card which cuts the price in half.
The gas stations would ask you if you had a card, and if you said you didn't want one, they'd scan one and throw it away. I assume it's because some higher up demands x percent new signups...for what?
In the end they are just going to track me by my credit card, so what's the whole point of this song and dance?