Assuming you're going alone, don't need a car where you're going, and have someone to move your a** around when you get there. I'm not dragging my kids on a bus between any of those destinations and then making someone drive us around the entire time. Does that make me stubborn and/or a moron?
Does Megabus drop you off near a car rental place? I hope so. Otherwise they're probably losing a lot of business.
San Antonio, Austin, and Dallas all have much superior transit options than Houston even if that isn't saying a lot.
Well in San Antonio it drops you on the Riverwalk and in New Orleans on Canal Street, so you don't need a car there. In Austin it drops you at the UT campus which is by Guadalupe Street which has numerous buses to downtown. In Dallas it drops you in downtown where all the DART trains stop. Houston is the biggest issue really.
To add to this I know in San Antonio there are numerous Hertz 24/7 stations even in the Riverwalk area, which is their version of Zipcar/Car2Go. Austin has ZipCar/Car2go all around the city too. I think Hertz 24/7 is in Houston too now. Not sure about New Orleans and Dallas.
Amtrak takes 5 hours between Houston and San Antonio, 9 hours between Houston and New Orleans, tends to show up behind schedule, and is $34 minimum one way.
I want to go from Houston to Dallas and take my wife. It costs $51 each round trip. ($102). I have to get to the megabus terminal in Houston. When i get to Dallas on their timetable (not mine), I need to rent a car. While going to/from Dallas, I cannot decide to stop at Collin Street Bakery or Buc-ees. Or, I can take my 25MPG car, pay roughly $75 for gas roundtrip, leave when I want to, stop when/where I want to, not rely on someone to get me to/from bus terminals, not need to spend $200+ renting a car. Why exactly would that make me stubborn or a moron?