[samatman]

> for example, why would a donut shop give receipts?

Because of members of a social club, whose turn it is to buy the donuts, wants to have it to give to the treasurer so that it can count against their monthly dues.

The more general answer is because, at this point in time, a receipt is universally expected. I'm not denying that businesses have internal reasons to hand them out, and keep a copy, I'm saying that customer demand played a role at the time this convention was established. They've become increasingly useless on the customer side, except for business expenses, where they remain vital.