I used to ask "can you give me a discount if I pay in cash?" and most of the times the merchant would say no. Then I stopped asking and started using only credit cards for at least earning some "rewards" back.

("rewards" purposely in quotes since it's not really a reward, but amex/visa/mastercard want us to think it is - there's no free lunch)

The proper term for these "rewards" is kickback.

In my country you pay extra (2.5%) at the checkout counter for using a credit card.

In my country that would be illegal. Here, the price is fixed first, and the customer has the right to choose any supported method of payment.

Merchants are free to offer more reward points or discount coupons for cash payments, though.

They advertise it as 'paid by merchant fees' but somewhere in a ledge or spreadsheet everyone makes a profit except the individual consumer. Maybe the prices are higher in general, maybe there are some consumers where more value is extracted than from others, but money doesn't appear out of thin air (except when you get into the whole derivatives gamble). Someone, somewhere, gets screwed over when a bank or credit company "gives" you money.