If you had to carry cash for small purchases that would remove the convenience of cards.
Buying a single pack of gum on a rewards credit card might lose the merchant money. They’ll make up for it in aggregate, but that transaction has a negative return. I understand the desire to limit how frequently they sell at a loss.
Credit card agreements used to require parity with cash and no minimums (as Visa and MasterCard had to create new buying habits). But recent laws have placed restrictions on those restrictions.
The Dodd-Frank Wall Street Reform and Consumer Protection Act of 2010 permits businesses to impose a minimum purchase amount of up to $10 for credit card use, but the minimum must be the same for all credit card issuers and payment card networks.