> So we’re going to see a price and by the time we get to the register all the prices will have changed?

I think the design of the system entails that the price you see and the price you pay would be the same. It's just that different customers are going to see different prices.

Then the question is how do they track you from the time you picked the item to the time you scan it. Which is what I was opining on.

> demands for price checks

What would that look like in modern commerce? There is no "big book" of prices. The best you can do is go back to the shelf and say the price is wrong.

Now you're debating which is the actual store price? The one on the shelf or the one on the computer? Stores are not generally obliged to honor mistaken prices although they may be in some states. Famously Arizona Iced tea is not actually 99c everywhere it's sold.

It's then a game of chicken and most consumers will probably lose.