In the US at least, it is their money. The Federal Reserve is a cabal of private bankers that produce the money we're forced to use.

I think in other nations, it probably still makes sense to think of the local fiat in that same way. We are not the regime (with the exception of any feds lurking in the comments).

Their money is fiat. Our money is, or soon will be, Bitcoin.

Depends on how you define "sound"

They don't always get bailed out, at least not entirely. During the last recession, when Detroit collapsed, the state of Michigan was just installing emergency officers in a bunch of cities to override the local mayors and manage the bankruptcy processes. There were also a few municipalities in CA that went through something like bankruptcy a few years later. That's my recollection anyway.

I think there's a real chance that we see some of the major cities, that have been hemorrhaging capital and labor, collapse under the weight of decades of mismanagement.