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How about internet buds? You haven't convinced me and just exchanging the word private for public does little to solve the issues.
So if N.A. is all private today how would anything be different? There would still be about 80,000 very crazy people in all the positions of power within any given private network. Again, saying the word private does little to solve the issue.
One has to solve the root causes of corruption and address those issues meaningfully with a high degree of efficacy and utility to have any real impact.
It was the private capitalist barons who wrecked havoc on Christian communities between 1850 and 1950. See the movie, There Will Be Blood, for an​ example of this kind of power abuse.

lol sure. TWD buds at least.
I'll convince you the government can do nothing right, by introducing the Calculation Problem, as laid out in:

To make a long story short, any organization that receives its revenues via compulsory payments, rather than consumer choice, will lack the accounting function of profit and loss. Profit is how a business determines whether it is serving consumer demand or not. Government services lack consumer choice as users and non-users alike are forced to pay. There are countless resources in the world that can be combined in a countless number of ways, to produce a countless number of consumer goods and services. How does a business know whether it's using scarce resources in the most value-productive way? And once it knows what to produce, how can it know how much to produce and whether it's producing that thing in a way that's least wasteful?

Profit.

Profit ratifies the firm's production and allocation decisions. Loss encourages the firm to rethink the whats and hows of its production decisions.

This way, waste persists for as little time as possible.

Because government does not have this important function of the market to rely on, they will never know whether they are utilizing labor and capital in the most productive way possible. They will never know with certainty what and how much services to provide. They just fumble in the dark and cave to the loudest of special interests, and consistently fail at the most simplest of tasks.