I'm not saying it'll cost the same, I'm saying it'll still be accessible. (Also, comfort level on a train is typically much better.)
And it'll properly price in externalities, which is not currently the case.
Also, just to quibble, I think the _total_ travel time is actually not that different considering you're supposed to get to the airport at least an hour early, and how accessible airports are to population centers relative to train stations.
If you had to catch a cab either two or from the airport, but could avoid it with a train, the costs you cite are suddenly about the same.