What exactly would a "privatized" military look like?
Would there be a big company called General Military, that would sell military services?
Who would buy these services? How would they be paid for?
What would happen if the company got a better deal from another country?
Say China says "We'll double what the US is paying you", is that it, are we defeated at the bargaining table?

I find the idea of heavily armed "private" armies a little discomforting, especially in a world where no one else has much in the way of firepower.
What happens if the leadership of the private military decide that they would rather run the country, who would defend the country against them?

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“ The subjects of every state ought to contribute towards the support of the government, as nearly as possible, in proportion to their respective abilities; that is, in proportion to the revenue which they respectively enjoy under the protection of the state.”

Adam Smith , The Wealth of Nations 1776

"We have always known that heedless self-interest was bad morals; we know now that it is bad economics"
FDR's second Inaugural Address