They want to harvest your data and sell it.

Well, yes. But they’re doing this anyway. If you’re paying with a card (and most people do), they’re using your credit card number as an identifier to track you across all the purchases you made across all their stores. These days, they may also be using facial recognition for the same purpose, to even catch the people paying with cash. Making rewards program memberships and the like illegal would barely slow down their data collection at all.

Well, you (and everyone else) are paying for it through retail markups and profit margins … but you’re going to be paying that anyway under capitalism.

What the store gets out of it is:

A) They hope their rewards program will motivate you to shop at their store, rather than going to any competitor’s, since you have a rewards card for their store and hopefully not the others. So the rewards program could increase their market share a bit, at the cost of a few discounts.

B) They’re using it to track you, of course. It provides more analytics for them to further optimize selling you shit, and they might also be selling the data to 3rd parties.

Why only for groceries?

In the interest of keeping markets fair, it should be illegal across the board to change prices depending on who the customer is*. The price is the price, as it should be in a free and fair market.

*Though I think I’d still allow for rewards/loyalty card programs and coupons given to frequent customers and that sort of thing – with the distinction being it’s something that the customer explicitly opts in to. And a restriction that these programs can only ever lower prices, never raise them.