I was not affected by the recent data 'breach' but I can see how difficult it would be.
My MBNA Emirates was compromised two years ago and I was informed only a day before travelling overseas. I did not have any other cards at that point and did not have time to get a new card.
Had to use my debit card and leave cash deposits in various countries and lost out on the exchange rate and also the miles.
I now carry at least 4 cards issued by various banks (Mastercard/Visa/ Amex/ Rupay) on each overseas trip.
I have always wondered why UK banks/card issuers do not have a system of sending an SMS whenever the card is used .
Many banks in the rest of the world have been doing it for years.
PS: I have Amex app set to push notifications and check it daily .