Do US credit card issuers take a loss on international transactions when offering no foreign transaction fees and no markup on the currency exchange?

Do US credit card issuers take a loss on international transactions when offering no foreign transaction fees and no markup on the currency exchange? Some US credit cards offer "no foreign transaction fees" (FTF) as a perk. When using these cards abroad, the customer is billed at the standard network exchange rate (e.g., Visa or Mastercard) with zero markup, and no additional percentage-based fees are added to the statement. I am curious about the backend economics for the issuing bank on these specific transactions. Assuming the cardholder pays their balance in full (generating no interest revenue for the bank), I wonder: Do cross-border transactions incur higher costs for the issuer? If so, does the issuer still turn a profit on the transaction itself? Or is the issuer essentially processing these specific international transactions at a loss, treating them as a loss leader subsidized by annual card fees and interest-paying customers?