Don't be fooled by those discounts, especially by COTO. Prices are inflated so they can offer them. You don't end up getting a discount. The credit card companies want you to use your card for everything.
Food isn't expensive if you have access to dollars. Argentines who earn pesos are feeling the pinch.
Compare prices in your neighborhood between the chain stores (DIA, COTO, JUMBO, NORTE, DISCO) and the independent groceries mainly owned by Chinese. That's how you'll find the best prices. The big stores buy larger quantities but don't offer lower prices because they have high overhead. I used to shop at COTO until I noticed the huge difference in prices at the local Chinese grocery where I can get in and out more quickly. They don't accept credit cards, and there is never a line.
I don't have a credit card, but I'm retired. COTO gives a 10% discount on Wed/Thurs if you say "jubilado" at checkout. No document required. It's not much, but it's something.