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.

You have airports that are pretty convenient to the city (assuming that's where you're going). Boston. SFO is at least on BART. The old Hong Kong airport. But newer airports tend to be pretty far out because they presumably need more land and that land isn't available near the city.

It's also because city residents will not, under any circumstances, allow a new airport to be built anywhere near them.

Trains don't need wings, so they're a lot easier to build tunnels for..

Yes, they are - if you count wings, which are the main point of a plane.

So as a reader one can assume that either a) I forgot about the wings (I guess I must be an idiot) or b) I am using a broader set of reference objects than simply "current passenger transportation modes". There are many man made objects much bigger than airplane wings. Fitting an aircraft carrier, or a container ship, or a skyscraper, moving under a city, would be much, much harder than fitting an airplane. Not to mention that if we strongly applied this engineering constraint, it's not beyond the realm of imagination that we could produce airliners with removable or foldable wings, or where the passenger compartment slides out, or tunnels with deep grooves for the wings, etc.