If private companies were more efficient than the public sector then you'd want to privatize the armed forces. The fact that no serious person argues for this tells you all you need to know.
Hi, Academi (formerly Blackwater) rep here, would you like to further privatize your war endeavors?
The argument against private armies has less to do with efficiency and more to do with dealing with coups from wannabe tyrants. If even "loyal to the state" armies can have internal schisms and take over the government, what can someone expect from an army whose sole reason to exist is "money"?
Yeah there are very good reasons why it's a stupid idea. It's equally stupid to privatize areas of strategic economic importance, such as energy, transport, core infrastructure etc. Which happens all the time. Arguably the army is the most important service for a state. If the private sector was innately more efficient you'd have thought the neolibs would be queueing up to flog it off.