The things do not fallback but rather propagate causing an avalanche. The only alternative to electronic payments which always boil down to some form of VISA or Mastercard card, is cash.
I do not have the information about what happened to the ATM's during the meltdown on Friday, but the bank branches where CrowdStrike had been deployed were rendered inoperable.
So, no, cash is not going to help.
Cash has a habit of running out from time to time, most annoyingly when it is needed and the amount of cash on hand is $0.50 – $1 short, hence the universal uptake of electronic payments. There is no going back.