Blackwater is a good example: they are not as good at fighting as an actual first-world army, or indeed as some of the insurgents they've gone up against. They are also deeply unpopular with the civilian populations of those countries, far more so than either professional armies or locally-raised forces.
Blackwater is simply the mercenary group that made the news, primarily because of a single massacre and their ranks being chiefly comprised of westerners. There were numerous other security companies that provided and provide local security to military and civilian installations that the world knows nothing about because either A) there were no massacres with them, or B) they hired mainly Ugandans/Argentinians/Afghanis/I'm sure there are a few nationalities I haven't seen (and from a Western news media perspective, massacres involving two sets of people who aren't Westerners aren't particularly newsworthy unless they are quite large). So in that regard, I would say that Blackwater is an exception rather than the rule.
In the longer term, as we've seen in Iraq, the conduct of mercenary forces and ill-disciplined regulars creates enough public outcry that it can force the newly-installed client government to turn against its liberator. This "turning against" needn't be in the sense of a military uprising; it might only be in the sense of revoking political ties and becoming a satellite of one's enemies instead, but that's hardly a good outcome.
Blaming private security firms for the difficulties the US had in Iraq isn't really accurate. Our issues sprung from the fact that 1) Representative democracy ran directly counter to the best interests of a small but relatively effective Sunni population that had governed the region for a very long time (from the Sunni side), and 2) the Iraqis always knew the US was leaving... and they always knew the Iranians would still be right next door (from the Shia side). The first insurgency (Saddam loyalist instigated) started before the negative press regarding security companies and largely created a demand for their use. The second insurgency revolved primarily around sectarian civil war, and was a result of many years of geographical mixing without resolving any of the underlying differences between tribes and religions. Once the strong and violent central authority that had kept those differences in check (namely the Iraqi military and secret police) was disbanded it became a free for all over money, territory and power. The US, private security firms and military, was more of a spectator caught in the middle of that one than the primary force, and the "sorting out" period resolved itself with an enormous amount of bloodshed that occurred with a US military force that was much too small to slow it down, much less stop it.
If this was the case in Stellaris, I wouldn't use them to pacify a newly-conquered planet if I actually wanted to keep that planet and its people. I also wouldn't use them if my goal was to stabilise the planet and turn it into a prosperous ally. I also wouldn't use them if I thought there would be real fighting, because that's what I have real soldiers for. I might, however, use them if I wanted to make the planet stop fighting against me and didn't really care what happened to it afterwards so long as it didn't involve me.
This also seems to be the attitude of the Americans in Iraq and the Saudis in Yemen.
So you use them primarily to augment your manpower in a way that isn't visible to your public and the world, as well as fill short term capability gaps. Nobody really cares if a contractor dies, but soldiers are newsworthy. Contractors also don't count against your troop numbers when those troop numbers are very carefully monitored by the news media. Finally, they can do things that you don't want to tie your combat troops up in, don't have the loggies to do for your either, but that still need to get done. Remember, every ECP that has to be defended means one less platoon going on patrol or going on raids. You don't need the best defending ECP's most of the time, but you do need
someone.
https://www.fas.org/sgp/crs/natsec/R43074.pdf
An interesting open source look at contracting. BLUF is though that we don't use contractors to comprise roughly 50% of our "workforce" in places like Iraq (they aren't there to fight) because we want to. We use them because it is a more politically palatable (and financially viable) choice than doubling the size of our military for a counterinsurgency campaign.
So one final point. I would argue that not using private contractors, at least in the context of COIN, would be at best a double edged sword. Why? Because when contractors shoot people they shouldn't because they are poorly trained, it creates some negative publicity that is spread out between the US and the firm, but the pictures at the end of the day are of people NOT in American uniforms. That really does make a difference. Taking boatloads of poorly trained conscripts (which is really your other alternative to using contractors) and putting them on the streets of Baghdad/Baqubah/Falluja/wherever is setting conditions for a series of poor decisions resulting in uniformed American soldiers (conscripts) shooting people they shouldn't. That really does make a significant difference. Especially since many of the contractors we have build up considerable experience or already have such experience when they are hired... something conscripts wouldn't have.
