The barrier of carrying a card allows the supermarket to give a discount to customers who are motivated by that, without needing to give the same discount to everyone.
The value of the tracking is probably irrelevant to how they set the price: it is not that loyalty card discounts have increased since tracking has become more valuable.
At the end of the day, I use the same credit card every time I shop, so I'm sure that they can harvest all their data from that. But I feel like it's a bit of a "fuck you" to the system that my loyalty card says I'm a 40 year old woman.
These supermarkets want to know if there is a correlation between you buying X frequently, and Y occasionally. They want to know if your profile is that of a bargain hunter or a premium gourmet hobby chef. Knowing all that, they can offer you tailored deals designed to nudge your spending behaviour one way or another, and they can determine if a specific store location should focus more on certain groups of customers.
At the supermarket I'm thinking of, with the 1-2% discount, there'll still be normal sale items that don't require the card, and then extra discounts that only the card gives you. Actually I just remembered the card earns you reward points as well (albeit slowly), so the total amount you "save" is indeed a little more.