How does that fix censorship concerns? The main issue is that political pressure campaigns has a lever over the entire payment processing sector because of cartel like behaviour. A public service could provide an alternative for sure but it'd have to be done very carefully and independent.
Actual government stuff is way more legally constrained than private sector stuff. It would be trivially to sue for freedom of speech if I was gov.
Public-private partnerships like chartered banks, and outright cartels like Visa MasterCard, are much more fruitful mechanisms for this sort of civil liberties abuse.