Oh I don't think it's a problem
I have an issue with - coining this now - bad geographic verisimilitude. Like abusing famous landmarks to create the impression of accurate location shooting. My favorite example is the opening of Hard Target, when some guy is being chased by the antagonist. One shot, he's on foot in the French Quarter; the next shot, he's running across the river with downtown in the distance. So, this guy either suddenly ran five miles across an automobile-only bridge or took the time to catch a leisurely ferry across the river. But something like Eyes Wide Shut, which is clearly trying to be somewhat surrealist, doesn't bother me at all.
Miller's Crossing doesn't actually mention the name of the city, but yeah it gives such strong Chicago-vibes that's what you assume.