>we still rely on private payment processors, credit card companies, which extract fees for a service that doesn't have any technical necessity anymore
The technical necessity is there; for your chase-backed visa card to pull money from chase and deposit it into your shop's citibank, there needs to be some infrastructure. Whether a private company or the government provides this infrastructure is another story.
(Although if the government provided you could argue that there would likely be even more political headaches that prevent what goes across the wire).
Bank transfers are a thing. They don't require an intermediary credit card company. The problem is that currently such a transfer is usually slow because of software/protocol issues.
The technical necessity is there; for your chase-backed visa card to pull money from chase and deposit it into your shop's citibank, there needs to be some infrastructure. Whether a private company or the government provides this infrastructure is another story.
(Although if the government provided you could argue that there would likely be even more political headaches that prevent what goes across the wire).