I agree with your reasoning but it's a bit deeper than "airplanes are 2x the speed of trains so therefore they are faster", and not just because airplanes fly a lot of extra distance for ATC reasons.
At major city airports you easily lose 2 hours with security, taxing around the airport in the airplane doing 5 mph, and boarding/deplaning. Not to mention any weather delays, and good luck if you have luggage.
Plus, most airports are not that close to the city center. Most train stations in the city center. I'm most familiar with NYC, but I can walk from my office to 3 train stations (Penn Station, PATH, Grand Central) in less than 15 minutes. The 3 airports are all an hour in a subway or 30 minutes in a $50 cab ride away. The airports are also more subject to traffic. The last time I flew to Florida from NYC, I spent more time on the ground getting to JFK, waiting to get on the plane, and waiting to take off to NYC than in the air.
With all that said, 200-300 mile trips make a lot of sense by train. Boston->NYC, NYC->DC by train make a lot more sense than airplanes even in the best weather. When the planes get slowed down by bad weather, forget it. Even Boston->DC by train makes a lot of sense, even today with our relatively crappy high speed rail.
I imagine a train up and down the east coast of florida, or the California coast with slightly better technology would do similiarly well.
But a train from NYC to Chicago or Denver makes no sense. And definitely not for NYC to LA. As soon as the portion of the flight cruising increases beyond an hour or two, it just kills a train.