Strong Customer Authentication (SCA) requirements coming into force in Sept 2019 are making card payments increasingly unattractive.
Payment Initiation (via PISPs, which Stripe undoubtedly will become) will offer free, instant, seamless push-based payments where fraud is essentially impossible (and the merchant isn't liable anyway).
Imagine having Cuvva's payment button pop you out to the Monzo app, hit accept, then immediately pop back and have paid. No card networks or fees involved. Just a simple Faster Payment directly from the customer's bank account to ours.
For in-person payments, I'd imagine a similar arrangement could be facilitated via Apple Pay.
May take non-EU countries a while to follow, but they surely will eventually. The days of CC companies are numbered.