Presumable the stuff I actually need to buy locally is the same as what other people need (milk, perishable items, meat, the occasional bottle of wine).

That just means the stores will have to be small (which is a benefit for them, since they have a smaller number of items in their inventory).

As for starting new types for stores? That happens surprisingly often, but obviously since most consumers don't give a hoot about who owns the store they shop at, it usually doesn't work.