I don't see it that way.
Being able to punish supernatural criminals in the USA would inevitable have to involve a treaty with the Fey Courts, the Vampire Courts or the White Council made in equal standing.
This is basically impossible.
If Mab were willing or able to keep her people from hunting humans for fun, sport or nourishment she would have done so long ago.
What means does the goverment have to pursue a Fetch in Arctis Tor, or even a Red Vamp in Chichen Itza?
Any serious attempt at law-enforcement against supernatural powers will most likely end in open war between the goverment in question and several supernatural powers and have terrible consequences for the entire world.
I think that for the fey at least it's a mix of needing some level of human involvement for various species and simply not caring about the consequences outside of that.
If a deal could be reached they wouldn't be able to break faith though; just exploit the wording ruthlessly. The mortals being aware enough to fight back might be something that makes them care enough to make a deal. Especially if they negotiate on a country by country basis and have different deals with each based on their capacity to resist.
I do agree that with some powers it'd come down to war. The white court would probably dodge it since they're sunk pretty deep into the people with power in their territory already, but if the red court still exists at that point they're basically made to press people's monster hunting button.
I do think you're right about wars breaking out though. The US would go for that over surrendering any sovereignty, or even the appearance that it'd done so.
At that point I think we'd basically have to choose a side; this under the table contractor stuff wouldn't fly anymore. Which could be an opportunity for us if we're inclined to go that direction.
Go all in with the feds and sign on with an actually clean supernatural division, work out way to the top because an exalt should just be that good, and become a national level power player in shaping the new world.
I'd rather not do that while things are still secret personally.
Edit:
The so-called "monopoly" on the use of force was bad in theory, and false in practice.
You're kind of arguing against the basis of every governmental system in existence here, and playing silly purist games about the monopoly on force.
It's never a perfect monopoly, but for governments like the US it's unquestionable (from a mundane perspective) that they're the strongest force and that the lesser ones have to comply. Your capacity to maintain such a state within your own territory is a big part of what goes into measuring the legitimacy of a government. Not all of it, but on a functional level you aren't a real government anymore if you lose the ability to enforce your rulings.
The basis of your point here is at best debatable, and more relevantly isn't one subscribed to by people outside of anarchist communes. Mortal governments the world over are going to act to attempt to preserve their monopoly on and exclusive legitimate right to use force where they can.
Bouncers kicking people out of bars isn't the same as systematic enforcement of laws across a nation's territory. The comparison is ridiculous, and no one will treat it that way.
Your bit about democracy is also nonsense. Seeing strange outside forces makes people band together and put aside their differences. Vampires in the night will simply make people put aside their politics to pick up stakes. Or at least manufacture them for people who can pick them up.