Earlier quoted context omitted.
Issuing banks typically add an FX fee to the cardholder for cross border transactions. Not always, but many times they do.
Even if the FX is notionally "free" they pick the rates. So they can set those rates to generate exactly the same profit for them as with fees. You will probably not see rates that are even competitive with a dodgy FX cash place at an airport, let alone with the numbers you've seen on financial networks for what FX transactions by banks cost, but you feel happy because there was "no fee".
You're crazy.
I have a Capital One account because they advertised "no foreign transaction fees". I checked on my foreign-currency payments and was always charged an amount that looked eerily similar to "1% more than you would have paid at the published exchange rate", so it's not clear to me why they say "no fee" and not "1% fee".
But the 1% fee that they actually have is very reasonable. An airport stall is in an entirely different league.