I'd be avoiding any place that did this out of principal.
I guess that is the worry for some supermarkets when trialling this - there will always be the local cost cutter or grocery store, butchers and corner shop that people could head to instead.
Likewise some chain could make a big deal out of advertising that they don't use dynamic pricing but "promise to keep the same low prices, guaranteed" etc...
Overall though it ought to increase efficiency if implemented widely - it isn't like there's not fierce competition between supermarkets. Certainly the rise of supermarkets and increases in efficiency have overall lead to our food/shipping in general being much cheaper.