You have never heard of private military companies? They are extensively used byvthe US mostly for non combat situations. They are very effective, for profit, and much less costly than the regular army.
Let's make it a bit more ridiculous and extreme. Would it be a good idea to privatize US nukes? What would profit incentive provide there?
Remember, we are discussing the claim "creating public institutions without a profit incentive is a disaster waiting to happen".
[citation needed] My understanding is that they are more expensive than uniformed soldiers.