This was something we started looking into when working on the TrueLayer integration, and I think the answer is that it varies depending on the provider.
For Amex I think the difficulty is that if you want to pay your card by bank transfer then you need to supply your full card number (PAN) as the payment reference. We’d have to see if the Amex API lets us read that (and whether we’re comfortable asking for customers to share that very sensitive data with us) before being able to build that feature.
From a purely technical perspective though? I don’t see why not!