In the UK, some supermarkets do this. At my nearest supermarket, they can have very large discounts (maybe 75% or more) when an item's expiry date is today, and

In the UK, some supermarkets do this. At my nearest supermarket, they can have very large discounts (maybe 75% or more) when an item's expiry date is today, and occasionally they do increase the discount over time like you suggested. Each time they change the price, they put a sticker with the new price and barcode over the old one, on every discounted item. The employee time required to do this is non-trivial. I imagine that in some places, stores would decide that it's not worth the effort, since a discount might not increase sales enough to match the reduced profit per item (especially in affluent areas where customers can easily afford the full-price item, and maybe turn their noses up at items near their expiration date).