It's not just a matter of needing the computational power, it's about needing global networking connectivity. If there are several isolated local copies of the blockchain around the world being used for local transactions, then they all diverge. If global connectivity is later restored all but one of those blockchains would be invalidated, meaning that transactions would be retroactively invalidated. If you sold stuff for bitcoins you might find that when global connectivity is restored some other copy of the blockchain is the winner, and the bitcoins you thought you had are no longer yours.
In other words, to validate a transaction and know that it won't be revoked retroactively later, you need world-wide connectivity at the time of the transaction.
If people trust a physical representation in the form of Casascius coins (https://www.casascius.com/) or similar, that's fine, but that depends on people recognizing and trusting those coins not to be counterfeit, since they're made of brass not gold or silver. If you're trying to buy stuff with brass coins that might be convertible to bitcoins some day if global internet connectivity is restored, and someone else is offering gold or silver Eagles, I think you're going to come up empty. If you're expecting a global meltdown you probably want to convert your bitcoins to gold or silver (and maybe some MREs and ammo) rather than to Casascius brass.
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