Private companies have economic incentives to charge as much as they can get away with and pass that excess to the owners of the company. This includes participating in collusion with peers and regulatory capture to artificially raise the rate in the market far beyond what efficiency would dictate.

Private companies are inefficient by definition when individuals are able to extract millions to billions of dollars from the market.

Is efficiency of the company the wrong metric in this case? Wouldn’t we rather have a market and prices reflect what it can bare rather than an open tab?

I agree, except with your last sentence. There are many examples of efficient organizations that extract billions from the market from willing participants.

What sort of definition of efficiency are you operating with? A system is not efficient if billions of dollars are "evaporating" out of the system.

Yes, the participants of those markets are various degrees of willingness. No, I do not agree that makes them efficient.

Computational complexity theorists hate this one simple trick! NP hard is a lie! You just have to assert that a given problem has been optimally computed. We all know that physics obeys the whims of politics. </s>

It's especially ironic because if markets actually worked the way the "free market" dogma supposes they do, central planning would also work.