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A small city would be essentially destroying its own airport by authorizing a convenient rail connection to a nearby bigger city’s airport.

Example: there is a train between Milwaukee and Chicago and it stops at MKE, but it will never stop at O’Hare, because that would be the end of MKE.

Technically you can take the Blue Line from O’Hare to downtown, making dozens of local stops, and then walk a few blocks with your luggage to Union Station, but by the time you get downtown you could be in Milwaukee already on a connecting flight. And those few outdoor blocks are a big deal in winter, dragging soft sided luggage through the slush is not fun.