Count two hours just getting to your plane and another hour waiting for your luggage, plus the usual flight delays and being stacked for landing, and a 200mph train would have a rather large distance that it could effectively cover faster than a plane if stops are infrequent and/or quick.
Let's say our 200mph train gets to average 100mph including stops. That's a 300-mile head start on the plane counting only the three hours above. Then the 600mph plane would cover that in 30 minutes, by which time the train would be another 50 miles out. The plane catches up again in a few minutes. So our train has at least a 350-mile radius for being faster than a plane. That's about Los Angeles to San Francisco.
Add to that the fact that it's easy to put a train station in the middle of the city (the usual destination) rather than way out where the airports usually are.
Cross-country wouldn't be bad either. Sure, it's three thousand miles, but you could go 200mph most of the time, especially in the Southwest. I'd give around 20 hours coast-to-coast.
During those hours, the ICE is comfy even in second class, and the dining cars are superb, with real, edible food, seating and real dishes (as mentioned) and metal utensils. You can get a cabin or row seats. You can walk around all you like without being too crowded. And it's fun to pass the time watching the scenery go by really fast. There are even displays at the front of the car to show you the current speed and computer kiosks where you can get a bunch of information.
That's how I'd travel if they had it here. More time in some cases, but a lot less stress.
Sounds like a win-win to me. Although it wouldn't matter to most, you could also have a designated smoking car. That's what was great throughout my travels in Europe, if I needed a smoke, I just stepped into the smoking(Pub)car. Have a pint and a smoke and you're ready to go back to your book or nap.
So who arrives in Pittsburgh first?
You're also assuming that the far higher number of stops for a high-speed train will only slow its average speed to 100mph. I'd bet against that, as well. Let's use your LA to SF example... you think there won't be stops in San Jose, Monterey, and San Luis Obispo (or Fresno, Modesto, and Bakersfield, if they don't use the coastal route)? Each stop will last for at least 20 minutes, more likely 30-40 (if not more for maintenance checks, handicapped passengers, bureaucratic requirements, lost children, etc). That adds about 90 minutes to the trip alone.
Even with instantaneous acceleration, that 400 mile trip at 200mph lasts 4 hours, minimum... and that's assuming that Berkeley, Pasadena, Long Beach, Anaheim and Oakland won't want their own stops as well.
But if you're so sure it can be done, then find the investors and make yourself a few hundred million.