Cities are climate islands full of imported trees and bushes. Parrots could not live in flat, cold, agricultural Illinois. But they can thrive in the City.
The much more colorful Carolina parakeet was native to Illinois and did just fine there for thousands of years, until it was exterminated.
Some parrots do quite well in cold climates. Quakers/Monk parakeets don’t depend on urban microclimates- have excellent, very thick plumage that keeps them as warm as ducks. They also have feathers that cover their nostrils, (as do ravens and woodpeckers), in the case of quakers aiding in containing heat.
Unlike other parrots, who nest in cavities, monk parakeets build large communal stick nests with the entrance near the bottom. They like urban areas because that is the place where they first escaped and, of course, because there are more French fries to be found there. They simply have not needed to disperse far beyond this first home due to the abundance of food and suitable structure upon which to build nests.Not to mention there are fewer predators.