And here was me thinking a Liver Bird was a young female Liverpudlian. 
I don’t follow this. What in particular stops it from being a general form for ‘-pool’ placenames? I don’t see anything surprising about Liverpudlian being the only one in the OED, because I wouldn’t expect every single town with an adjective to get listed.
And just to explain all of the humor out of the joke, “Gotham” means “Goat town”, suggesting as rural, backward and out of the way a village as you could get. It was sort of like the more current term “Hicksville,” which suggests the village where all of the rural hicks live (though it is also a perfectly lovely suburban town on Long Island).
Washington Irving’s humor was in referring to the bustling city of New York as the prototypical tiny goat farming village where the villagers are utterly unsophisticated rural fools. Ironically, this jest has changed the word “Gotham” to mean a major metropolis, not a rural backwater.
Not so much a joke than an insult. “Sooners” were, essentially, cheats. It’s similar to Missourians being proud of being called the “Show Me” state when the original meaning was that they were too stupid to understand things without a concrete example.
Yeah, but that one isn’t based on the place name at all, rather on an historical event.
I’m originally from East Liverpool, Ohio, and we did indeed refer to ourselves as “East Liverpudlians.”
There are several theories as to how “Hoosiers” came to be associated with the stalwart yeomen of Indiana. “Suckers” was a Civil War-era term for American Midwesterners, IIRC, before it took on the connotation of an easily-fooled person.