But then, who's going to be that concerned or bored enough to actually do the checking - ?
11 years ago I was made redundant and had a few weeks with no work. As I a,ways do the shopping anyway, I took to it with extra vigour. We always shop in Asda, a fair priced shop imo. I knew what stuff cost, I've been doing it for years and started picking up odd bits from Aldi, comparing the receipt with Asdas offerings...and vice versa, so I was getting the best price wherever possible.
I came to the conclusion I could save about 10% on a weekly shop by splitting it between the two, but the extra time and effort made it too much effort tbh, double the time, double the fuel.
You can save money but you have to put the effort in...and a fair but of effort. You're not going to get a week's shop cheaper in one place or the other, you have to cherry pick between the two.
If you could really be bothered, I suppose it could work....