The
real problem is that, practically speaking, you still need a car once you arrive in either Denver or Houston (because of the way American cities are built).
That implies renting a car at your destination if you ride the train, which eats the time and cost savings (and then some) of taking the train. So why not just use your own car and save the hassle?
Also, non-stop flights on that route have a scheduled time of less than 2.5 hours. Most flight schedules are padded these days to avoid fines for late arrivals, so it's hard to see that the train will be faster, even accounting for TSA. You'd have to make assumptions that don't really hold for the US--like getting to the train stations is faster than getting to the airport. For Houston in particular, the two airports on opposite sides of the city center make this particularly unlikely for a large fraction of the population.
Edit to add:
I also think that 4 hours is fairly optimistic for a train between Houston and Denver. That implies a non-stop train running at a constant 350 km/h or 220 mph on the great circle between those two cities. According to wikipedia, the fastest scheduled average speed of a TGV is only 280 km/h (with stops). So that's really closer to a 5.5 hour journey, which I think reinforces the point that it isn't competitive with air travel.