That's what we do with much of our weapons systems and military supplies. Lockheed-Martin, Boeing, Pratt-Whitney, etc. are private firms that the military contracts with.
Granted going all the way with privitazation the military would not likely work. But we do privatize certain aspects of it.
No analogy whatsoever. Does Boeing provide "military consultants" as pilots ? Do we have "Wild Geese" or mercenary units ?
A lot of libertarian nonsense romantically assumes that a capitalist society will just plain magically more militarily effective than an authoritarian society. That is romantic nonsense. The values of a good soldier are duty, obedience, order, discipline, courage, and self-sacrifice. These are not free market libertarian values. They are authoritarian values.
We only privatize the procurement end of it, not the actual military forces.