> You will probably not see rates that are even competitive with a dodgy FX cash place at an airport

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.