I disagree that private ownership of payment processors means the government is losing control of it's currency. I see Visa, MC, and banks in general as an abstraction of the dollar rather than a replacement for it. When I use a card or bank wire to transfer money I'm still technically sending dollars from one entity to another.

Since the gold standard has already proven to be too unstable, and cryptocurrencies haven't proven to be stable enough yet, I believe the only competition for the dollar is other nations' currencies. And determining which nation's currency will be the world standard is typically based on who has the strongest military and economy.