Getting rid of payment processors would benefit just about everyone. Only benefit they have is insurance.
At ~$30,000 a year in credit card spending I'm throwing that amount away in credit card fees every two and a half years. I'm perfectly capable of and would prefer the option to self-insure, thank you very much.
Ultimately insurance always has a negative expected value for the average consumer. It makes sense to pay the vig to insure against catastrophic events like a car crash or a house fire, but insuring my daily credit card purchases like takeout meals, groceries, and gas is stupid.
However... bitcoin does allow new insurance providers to pop up - the insurance provider no longer has to be the same entity that holds your cash (your bank) or provides payment processing services. They could experiment with new models - multi-key escrow until service delivered, an "approved store" model where they'll provide insurance on purchases from stores that they've checked out without ever having to touch the money themselves, or more. This could all be cheaper than what your processor + bank combination costs, potentially.
The thing is... that's not really good enough for customers. Nobody thinks enough about a few pennies per purchase to pick up a whole new currency.