Could, in theory. In practice, how do you implement and maintain that given there will be more than one person in the aisle looking at the price tags? Or that if two people see different prices, there are going to be two very angry people yelling at customer service? How will they advertise sales? How will they advertise?
Good points. As always, in theory there is no difference in theory and the real world, in the real world there is.
Right now, it's more of a hypothetical to cause a lot of handwringing, and likely more trouble than it's worth; since in the end I suspect the price difference would be so small that the costs to do it outweigh the benefits. For multiple shoppers they'd probably need to show the lowest, for example, so there would be no advantage to it. Who knows if it will ever happen.
One way to deal with some issues is to get rid of shelf tags and do all pricing in app, but that has its own issues; from people who don't use apps to allowing was price comparisons between shoppers in the aisle.
Personally, I'd rather see them use such data to offer discounts real time in app, since that would give me the ability to decide if I want to use it or not.
And what about Instacart?
That might be easier since they know the customer and buying habits, so targeting would be easier if ordered in app. (I've never used Instacart)