In most of Europe at least there are strict laws on pricing so if you make a discount, it can't just time out after 10 minutes, it needs to last the end of the business day or until the stock is depleted.
These stric pricing regulations is probably why electronic shelf labels were invented in Europe, to make sure there will be no discrepancy between the price on the shelf/discount and the price on the register, otherwise the store is liable.
Which in turn makes dynamic pricing even less attractive for the shop.
If they decrease the price, then there are some shoppers with the item currently in their cart who will pay less for the item than they expected to pay.
But the reverse is disallowed by law.
Which means that for every price change, the shop effectively loses out a little. Better not change prices too frequently!
The idea is to do a discount towards the end of the day to help clear stock that would otherwise go to waste because it has a short shelf life. Supermarkets do this all the time, but it generally involves an employee going around manually relabelling produce.
I would hate to put something in my cart that was $5 at the time I put it into my cart only to have it be $8 by the time I get to the till.