Houston-Dallas is a very high-volume city pair forming one leg of the triangle, of length around 250 miles. People do fly on this route, but most people don't, because between the airports' relatively inconvenient location (especially Houston's), security, delays, etc., it doesn't save you that much time. So most people just drive. But driving is just far enough, and stress/traffic-filled enough, that many people who drive that route regularly hate doing so (it takes 4-6 hours, depending on how good a day you're having, and much of that is with wall-to-wall traffic containing a heavy volume of trailer trucks in the mix). I've done it many times myself, and I'd love to take a train instead. For me personally, it wouldn't even have to be that fast: if the train could get me there reliably in 3 hours (i.e. average speed 85 mph, not even talking about Shinkansen speeds), I'd be very satisfied. Related things can be said about the other two legs of the triangle: San Antonio - Houston (200 miles) and the San Antonio - Austin - Dallas corridor (80+195 = 275 miles).
The topography here is also more friendly to rail than, for example, LA-SF, being mostly flat and open and with shorter distances. But unfortunately the state-level political geography is less friendly (at a local level rail is popular in all four of these cities, but the state is another matter).
The train from Albany to NYC is at or near capacity daily, although it's only 150 miles. Similar use case in many ways... It's enough of a pain to drive that people want to avoid it, and it's better than a car to go to Manhattan.
My uncle used to fly LGA to BOS a couple of times a week... I betcha that train trip is shorter now given the security and other nonsense associated with flying.
And Amtrak does offer an auto train though from Virginia to Florida.
I like the train but I don't assume it's a particularly economic option.
Any trip where people fly is a rail candidate. The hassle and bullshit associated with flying is high and getting higher.
We subsidize highways and air travel at the expense of other ground options. It shouldn't be 70% cheaper for me to drive my family to Florida or the Carolinas for vacation from NY vs air or rail. But it is.
Hundreds of thousands, if not millions, do that I95 trip every year. There are dozens of corridors like that.