I hope those "private contractors" are aware how mercenaries can be treated under the Geneva Convention 😟. While some might see combat, that's probably atypical. I was in the Army (a tech field) four decades ago. While I was never a contractor, I worked with them, and indeed could have been one upon discharge. Why do contractors exist? For several reasons. In the first place, generally speaking, government and especially military treats you like shit. Especially so in the military: you waive many rights when you sign on and you are subject to military discipline (sometimes even applies to civilians). Civilian workers might be treated better, of course. But the big reason is probably pay. Simply put, the government has never paid well and while they give bonuses and rewards for some special skills, in practice they probably don't compensate in line with a person's talents. For those who served in a highly technical specialty then, they often have been trained at great expense by the government/military, did their time, and often choose discharge. Also, for many skills they often hold a security clearance, itself a marketable asset. Then they may have the option to be a civilian contractor or a DoD Civilian (if the benefits are agreeable). They'll make many multiples the salary the military paid them. Note that what I've just described is mostly the techs, not likely to be doing real soldiering.
Now I enter an area in which I have no experience, only hearsay. Ah, but pity the "real" soldier, the infantryman or the Marine, or more likely an elite like a SEAL. These guys are closer to the traditional definition of a solider. Not to put too fine a point on it, they are trained to defend or kill. Some of them may have done some of that. These guys can find post-enlistment work too, but it's likely to be more shadowy stuff. The pay may be quite good, but the risks are at times at least very high. THESE are the expendables, that do the dirty work of intelligence agencies and other shadowy groups. Shed a tear if you must for the grunts, they are often doing very dangerous work, but at least they are well paid for their trouble.