Even now Chicago absolutely refuses to permit any public transit entering/exiting the airport unless they control it. The one they dont control (Metra) doesnt stop on airport property. Its way out in the rental car return lots and you have to change trains.
The problem with the Metra line isn't that it doesn't actually enter the airport, it's that there's only infrequent rush hour service on that line, and none on the weekends, and that's on the freight company that owns the line, not the City of Chicago. And even the people mover extension will be a better solution than the current option (taking a shuttle bus from the station).
Its also why they object to the third airport ( which is a different subject) and said they will file suit if it carries the name "Chicago" on it.
(a) Gary renamed their airport "Gary/Chicago" with no issues, (b) the obstacle to a third airport is the fact that United and American refuse to use it. Not that I blame them, both they and the airlines they merged with tried service to MDW, and couldn't get it to work.