We do, it's just very limited. Actually in Austin I think you could have pulled it off. You could have taken the Texas Eagle to San Antonio, then the Sunset Limited to New Orleans. It would have taken 27 hours and the Sunset Limited only runs 3 times a week, so if you departed Monday at 6:30 pm you'd be in NO Tuesday at 9:40 pm. Bon Voyage!
Just kidding. As a rail fan, it bugs me, too. My wife and I spent two weeks in Germany, visiting multiple cities, and we used a private car once (a relative gave us a ride) and a taxi once. Otherwise it was all trains and the occasional city bus, plus one motorcoach that took us to Neuschwanstein. It was pretty nice.