Crypto solves an existing problem with moving money over the Swift Network or the ACH network: it's slow and very expensive.
Normally, sending money cross-border relies on third parties like Western Union or MoneyGram that often take up to 10% in fees and FX conversion fees. With blockchain settlement, like the one on the Ripple Network, the fees would be at most a few cents and near-instant settlement, versus the 1-3 days of settlement via the fiat route.
Why would AMEX be interested?
Simply put, they are exploring a more efficient way to settle cross-border payments. Starting with their business customers for now, and eventually could be embedded into the daily settlement that the AMEX network does globally.
American Express partnered with Ripple to route business payments on its FXIP platform through Ripple's enterprise blockchain network. Payments are settled in real time, cross-border fees are dramatically reduced, and users don't need to know anything about blockchain to benefit.
The bigger picture
Joining Apple, Amex becomes the second large publicly traded company to start operating payments on blockchain — specifically on Ripple. This pattern of large traditional financial institutions quietly integrating blockchain infrastructure for back-end efficiency is how mainstream adoption actually happens. Not with fanfare — with settlements.