In name only. Even going back to times when each city had its own currency, there was always an administrative class. Always.Currency existed long before the public sector.
And they worked for the rulers. Setting laws, setting the value of currency, resolving disputes.
You have some weird idea that everybody can function just fine without any kind of administrative or law-giving class, and that private companies can substitute ???? (something?) for all the legal codes and everything else we've developed over millennia.
I'm not sure how it would work, and I suspect it wouldn't. Would be some kind of wild west where CEOs behaved like the mafia, most likely.