Agreed, pretty much every physical operation (stores, logistics, etc) should have plans to continue operating when their IT is down. Losing access to dynamic pricing and loyalty discounts is better than closing up entirely.
You could still fraud hit them in this circumstance, but they have some kind of info printed on your card with your name on it and how long you've been a member, and somewhere in the background, a phone# and address.
If one wanted to commit retail crime, easier to just take stuff and walk out without paying.
Might lose some payments to overdrafts or cancelled cards. But they lived with that with credit cards up until 2000ish.
Buy-on-board on Aircraft and trains take advantage of this.
Offline payments is baked into EMV payments. It can at least verify the PIN and that the card was valid at its last phone-home.
https://www.google.com/search?q=mastercard+emv+offline+payme...