Here in Norway, what is called the "competition authority"(https://konkurransetilsynet.no/norwegian-competition-authori...), is frequently critical to open and transparent (food) price information for that exact reason.

The rationale is that if all prices are out there in the open, consumers will end up paying a higher price, as the actors (supermarkets) will end up pricing their stuff equally, at a point where everyone makes a maximum profit.

For years said supermarkets have employed "price hunters", which are just people that go to competitor stores and register the prices of everything.

Here in Norway you will oftentimes notice that supermarket A will have sale/rebates on certain items one week, then the next week or after supermarket B will have something similar, to attract customers.