I think it is more akin to the entire economic arm of governments. If a country put their tradeable assets in one of these, it would be the end of tyrants collecting taxes to pay for the machinery that oppresses people into paying more taxes.
A legal, licensed corporation is not “private” in any meaningful sense; it is compliant to and works as a shard of the government’s economic/legal code.
That would be economic democracy, as the people as a whole can fund an NHS and even tax collection, prisons and an oppressive legal system and a sham “democratic” party system of “representation” if they choose to.
All running on top of the “money” (trade) paradigm still. Nothing too unfamiliar.