But, for me, I will be staying with the cards until the chargeback/dispute schemes match up on bank transfers. I don't want to have to go to the small claims court if I have a problem.
I wish. PSD2 will do nothing for consumers and won't hurt CC companies in the slightest. The requirements to actually be able to use the PSD2 APIs are insane. The only companies who will be able to use them are big players like banks, CC companies, large payment processors and large IT companies like Google/MS/IBM/Apple.
Something similar (but not quite identical) exists for direct debits called the direct debit guarantee.
Some sibling comments echo that this is underway in Europe. In America, the credit part of "credit card" is relevant. Many purchases on CC's here are intended as short-term (or longer) loans. (Something like 40% of American credit card holders carry a balance.) Direct debit from a bank account does not (and cannot) fulfill this use case.
Sure it’s sad that we no longer get air miles etc. But the reality is that we never should have in the first place - was a symptom of a nonsensical system.
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.