The issue is not how complicated and difficult such an endeavor is (and you rightly identify it as such).
The issue is, if we're going to do this heavy lifting anyway, might we do it in a way that doesn't involve theft ?
Expropriation usually involves paying the owners so it isn't theft, its just the government buying out the stocks just like a private corporation would. Are you saying Elon musk stole twitter? That is the same thing.
Anyway, here since this is shared between countries its better to just regulate what these processors can do, like the EU does when they regulate how large payment processing fees can be etc. Since its used for international trade no single country can own it.
It's not at all the same thing.
Twitter could have said no.
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.