So called “shadow work” is becoming more prevalent. When you choose to self checkout at a grocery store you’re essentially doing work for free (scanning and bagging your own groceries) in place of a paid cashier and bagger.
One would assume that in a sufficiently competitive market (for examples, certainly in the UK, supermarkets), this then gets passed on in terms of price cuts.
I severely doubt it's the case. Besides, businesses aren't typically interested in having a competitive market anyways. It's probably more profitable to not lower prices at all and lobby to make it harder for competitors to lower prices . . . or just conspire with major competitors to keep them higher. Both actions have a strong historical precedent in US markets, at least.