The Faerie Queen system may have actually been an Outsider plot to weaken the defenses of the Outer Gates in the long term by isolating the Fey, the footsoldiers in the war to protect reality, from any need to be diplomatic with the rest of reality thus allowing for a the Needs of the Many mentality to ossify in Fae Courts and leave them less capable of making alliances or figuring out a better system than the one currently in use.
If they had anything approximating that level of influence then reality would be dead by now.
I also wouldn't say they're bad at their jobs either, since reality still exists and the troubles of canon are the culmination of centuries of planning that you'll note didn't actually work out for Nemesis. They're far from perfect, but with what they're up against genuine incompetence at their core tasks would be fatal.
The more likely cause is the same as that of many other systemic problems; compromises necessary in the past compounding as they roll downhill from generation to generation.
As to the inability to manage relationships stuff? You're flat wrong there. They're the most diplomatically involved faction. They do business with everyone and everyone does business with them. There's a reason that it's the Unseelie Accords not the Wizard Pact, and that it has precisely zero meaningful competition.
You don't have to like them, in fact I'd say you shouldn't because they're assholes. You can also take philosophical issues with the narrative Butcher is pushing by making them like this and pushing them as effective, but you can't deny the state of the board for canon.
I don't like the horrific things they do and want to stop them as much as anyone here, but being awful isn't the same as being incapable* and a vast majority of the world they're operating in doesn't give a shit about the issues that make them a problem from a mortal perspective.
* To be clear, I'm not saying what they do is implicitly necessary or justified, just that they're capable of doing the job and aren't impulse driven idiots rotting at their posts.