My suspicion on this is that stores offer "reward cards" so they can get you to sign something that allows them to gather and sell your data.
Now your loyalty card data is worth twice as much. Once to the retailer for internal marketing, targeting, purchasing, etc... and again selling it to outside parties.
There's a reason they got so dominant over here - they were simply way ahead of the game on offering what their customers actually wanted, because they were the only people who actually had a clue.
That has of course changed now.
This is simply not true with respect to the big retailers in the US. This started as far back as '06, though the details of the implementation have changed a bit.