I generally pay my account by electronic transfer or similar, but on occasion I have been leaving a country with no expectation of returning there soon.
If there was an Amex office there, I would pay most of my remaining currency against my card. Even if the rate was poor, it was better than having a fair amount of otherwise useless currency.

Now, it seems that I won't be able to do this any longer.

How long till I can't pick up a new replacement card at an airport Amex desk before I fly out? Come to think of it, does Amex still have many airport desks like they used to?