Credit cards aren't very widespread here. When I say "credit" I mean "credit or debit", but it doesn't matter at all for this debate. If you don't exercise your right to pay cash, you'll lose it, and then it won't matter whose money it is, you won't be able to pay for anything without the bank letting you.
Some places I have visited here have a "no credit card" policy. They accept debit. Credit card transactions pay higher fees and are easier to chargeback
"No cards" is also spelled "cash only" ("Solo efectivo")