Not directly, but while it's possible there is(on paper) a CPS or similar organization while civilization crumbles around them, it's one of the organizations whose power(in practical terms) and financing would be cut first, so it being a powerful and well funded organization in canon, means that things must be pretty good for society as a whole, even if not necessarily for all parts of it.
At the same time stuff like the Birdcage, S9 (especially before Manton joined them, i.e before Cauldron got involved), the boat graveyard indicates society is in a pretty bad situation (especially that last, as it means there isn't financial interest to remove the ships).
I'm not saying that they can't exist at the same time as CPS, but they do indicate a very static situation, despite the fact that things should be either rapidly collapsing (if you got to the point of the S9 wandering around with impunity) or rapidly improving (if they had the spare resources to support charities like CPS).
"Civilization" is not crumbling in a meaningful sense inside the USA. Civilization - the mechanisms and institutions of social control such as police, taxation, telephone networks, etc - by all appearance continue to function within the world of Worm, at least inside of the United States.
The Slaughterhouse Nine are a rare, one-off group, thus their enormous reputation in setting, the fact that every member is preemptively shoot-on-sight, and their leader and fulcrum has one of the most OP defensive powers in the entire setting. If there were lots of groups like the S9, then I would agree with you, you couldn't run the country any more, but there aren't, and the S9 themselves hemorrhage members ridiculously fast.
The Birdcage is actually a mechanism of
reinforcing social control. We wouldn't say that the historical USA should have disbanded all social services because they had to build Alcatraz, would we? The government of Worm has the desire and capacity to throw all these people into prison. That suggests it's working.
With the Boat Graveyard, I don't think Brockton Bay is meant to be an economically normal city, but besides which, the collapse in its import/export industry also lead to, quote: "The richest and most resourceful people in town had managed to make more money, turning the city's resources towards tech and banking, but all of the people who had been employed on the ships and in the warehouses had few options left to them." (
Gestation 1.3) That doesn't exactly sound like a city in economic free fall unable to reinvest, it sounds like they didn't bother because the people with the money decided it wouldn't be worth it and they should do other stuff with their money instead.
