The “no transaction cost” claim is doing a lot of heavy lifting here. Cash may feel free to the person handing over a coin, but only because the costs are hidden upstream. Someone has to produce those notes and coins, swap out designs to keep ahead of counterfeiters, move them around in armored vans, count and recount them in tills, reconcile them at the bank, and insure against theft along the way. None of that is costless.

In fact, many retailers will tell you that cash is more expensive to handle than card, because every deposit requires staff time and often explicit bank fees. Society also pays indirectly through tax evasion and black-market activity, which cash enables far more easily than digital systems.

You’re right that cash is robust in a blackout, and there’s something elegant about a technology that works offline, peer-to-peer, and without needing servers to stay up. But the idea that it has no transaction costs is not realistic.

Most of the cost of currency is up-front in it's production and initial distribution. The cost of handling it is also mostly up front (purchasing a wallet to hold it, buying a cash register with a drawer for the bills and coins). The transactional costs are things like taking it to the bank for depositing. But if you have cash to deposit - your business is probably doing things right and this is negligible.