Before you go abroad you could notify your bank. Then in period you declared you are abroad they should lower expectation from "in person and ID" to phone call and other means of verification. After that period you are automatically back to normal security.
That is for example how my debit card works. If I want to use it abroad I have to turn that feature on for whatever time I am abroad.
In Europe you have a telephone PIN codes, you have number generators on the app. There are lots of ways to authenticate yourself. IN Europe you no longer need to tell them whether you're abroad or not; I guess the ML algo's that monitor for fraud are so much better than before that this isn't needed.
Losing a bank card isn't as critical as losing a phone # so companies have to act quickly. Think about it - Can you live without your bank card for few days vs living without your #
I think we just need to be prepared for these sorts of things. Travel with cash, your debit card, and one or two credit cards. If you can afford it, have a backup SIM (Twilio sells SIM cards for about $3 and the cost to keep them activated is $1/mo, and nothing more if you don't use it [0]). Use a Twilio or Google Voice number that you don't use for anything else for 2FA or account recovery for services that require a phone number (some providers reject these numbers, but many will accept them).
[0] Full disclosure: I work at Twilio and built the first version of the wireless product, so I'm a bit biased.
