Imagine this potential future with me. At first, it's just Amex. Then, to remain competitive, other major card vendors do something similar. Most of us (developers) still use something like Stripe for simplicity, but libraries start popping up that abstract away the vendor-specific APIs and make it easy to use them. Long term, though, as more and more payments are handled electronically and online, this opens the doo…
However - I don't think you'll see a proliferation of new payment methods. The biggest problem here would be fraud mitigation, so it'd need to be a payment provider the merchant deems trustworthy enough.
Interesting times ahead. Amex are just doing the bare minimum to keep up here.