For many people, going to a store the same day is completely impossible (not having a store within reasonable distance that stocks any similar product).
This is not just rural areas, either: even in major cities items can be delivered faster than the time it would take to find a store that carried the item, go to the store, get it, and come home again. It's really only suburban areas with a high density of big-box retail that even have the option to "go out and get something" immediately.
Amusingly, it's also only in these suburban areas where next day delivery even exists to compete. As an anecdote, living in the downtown of a major American city (population > 1million), the average Amazon delivery time is roughly 3 days, and last mile deliveries are all delegated to the USPS which adds significant time.
