I don't understand how this would work. If the government created some entity to handle processing payments (or whatever), I assume it would be a publicly funded non-profit, since there is precedent for that. How much funding does it get? Where does that money come from? How does it compete with the existing massively powerful corporations? What incentives does the government entity have to compete? What happens if it goes bankrupt or is purchased? What happens to whatever capital was used to fund it?

It just seems like the government entity would need to actively engage with seeking profits or just existing to artificially lower costs. I don't think the majority of people would want the government to have a for-profit arm that exists to compete with businesses, and I don't think corporations would just play nice.

I'd say that USPS is the closest example of this, and it's a pretty good example of how things can go wrong as well. The active attack against the postal service to try to privatize it is terrible. It will do nothing but continue to isolate power to the ultra wealthy and make people's lives worse. For-profit corporations and the government just have (or ought to have) fundamentally different incentives to exist.

I'd be curious to know of any examples of this working well. I don't mean to be so antagonistic, I just am really struggling to understand how this could work in any way.