Real costs are probably higher than you expect. Sure, it's so cheap it might as well be free to write a program that debits one number and increases another and run it a few billion times, but reliable financial systems require more than that. Consider what it takes not just to implement a chargeback, but to be able to implement a chargeback, and to be able to stand behind it legally, and to be able to defend against lawsuits, to be able to prove compliance with various regulations, etc etc. Everything looks easy from the outside.
I don't see any compelling reason to think the government would intrinsically do any better, it would just move the costs around and probably incur more of them overall when the full accounting was made, which it never would be, because who can regulate the regulators?
Is there any evidence that there is a competitive market driving the prices down though? Looks like this regulation was designed to push down costs by fiat, but people wanted to keep their profit margins and shifted the costs, so no worse than what you are saying the government would do. The government should be trying to design cmpetition into the system.
I don't see any compelling reason to think the government would intrinsically do any better, it would just move the costs around and probably incur more of them overall when the full accounting was made, which it never would be, because who can regulate the regulators?