Yes that is correct, the carrot Kroger and other grocers waive with the discount via loyalty card would tie the customer back. Which is why I would expect Kroger to cave before Walmart or Target, since those two probably don't want to be sucked down the loyalty card path. Regarding loyalty cards though, yes that doesn't bother me as I toss them in the bin after a couple weeks and/or using up the gas points.
It probably won't matter in a few years anyway, as the trade war with China, and lack of a workforce to deliver produce in the US, will probably destroy any retail business based on delivering cheap goods to market.