This isn't government setting prices. It's just government outlawing a certain form of price discrimination. It's forbidding sellers from transferring consumer surplus to themselves by charging a higher price to customers that would be willing to pay a higher price for the same item. But the item is still available to buyers that wouldn't want to pay the higher price--at the lower price. The grocery stores aren't going to raise the overall price to compensate for losing the ability to price discriminate: that would result in less profit for them. Whether they will try to find other ways of increasing their profit over what they get when every customer pays the price that's equal to their marginal cost, is a different question.

Somehow we did just fine without real-time per-customer price discrimination.