Denver's airport is apart from the actual city, and there are light rail lines connecting it with downtown. That system... does not work very well, owing to crappy light rail and the fact that most people still aren't where they need to be even if they took that to Union Station.
If you're suggesting this hypothetical giant tunnel would actually have the planes taxiing all the way to a whole airport underneath a city... I don't see that solving more problems than it would create.