Well the problem with some "really rich private corporation" ruling over everything, is no different than some really rich king ruling over everything. We'd just go back to feudalism.
In fact we really are going back to feudalism, since the people with the most money and economic power right now are the land-owners and bankers.
Adam Smith didn't envision some anarcho-capitalist libertarian dream land when he talked about the "invisible hand", he envisioned a capitalist economic system that is managed under fair rules. That's why he wrote his book "Wealth of Nations", and not "Wealth of Individuals". He wanted to know how to make nations richer.