Hm, I am equidistant from 3 different grocers and sometimes 15 dollar steaks are marked down to 10. I think you're right with a variered enough basket the sales will be a wash but maybe if I let the algorithm decide what my diet is that week based on what's discounted the most I could save some dollars. The thing that actually keeps me loyal to one store is I'm familiar with the floor plan so it doesn't take 5 minutes to find the hot sauce, so I would love a wayfinder for unfamiliar stores. Could be a good app for ambient competing / meta raybans.
depends on where you live. in european cities you tend to have multiple grocery stores within walking distance from each other. also you don't have to go to all of them on the same day. i delay buying certain things until i have a chance to go to the place where those are cheaper. it just takes a bit planning ahead.