The API doesn't have any additional fraud exposure.

The fraud exposure is due to identifying information, or access therein, being stored on and/or directly provided by the client in this model. Existing payment methods do not store billing information on the client devices as they are assumed to be untrusted.

  Also, all major card networks - Visa,
  MasterCard, AmEx - and many payment processors
  - Stripe, Worldpay, etc - all actively
  participate.

Card networks are not banks. Stripe is not a bank. Worldpay may be (I've never heard of them), but for the sake of discussion, I'll assume they are not a bank.

Banks are the CC account issuers and the processors "on the rails" of payment networks (Visa, MasterCard, Amex). Whether or not an ISO/VAR/merchant (Stripe, PayPal, eBay, Apple, Google, Amazon, etc.) wants this type of API is immaterial. If the banks aren't comfortable with it, someone is going to eat their discount rate hike (yes, ultimately this is the customer, but I'm talking about entities directly impacted by the hike).