As someone who has basically split his lifetime in San Antonio and Austin, I agree that the distance is too great to reliably expect the already established fan-base in San Antonio to travel to Austin.
I'm a die-hard Spurs fan...always have been, always will be. When I lived in San Antonio, I would usually go to 3-5 games a year.
Now that I'm living in north Austin, I'm lucky to make it to one or two games a year because it's an entirely different commitment.
I have to decide if I want to spend 2 hours each way in high traffic times, or pay out for a hotel in SA and make a trip of it. Either way, it's a lot more planning and money spent rather than just checking to see if some tickets are available for a random game or whatever and driving 15 minutes to get there.
If the Spurs were really to commit to moving to Austin, they'd have to be fairly certain that they could establish an entirely new fan base here because I guarantee the average Spurs fan isn't going to make that trip regularly. And as I mentioned before, you would be trying to sell a new team in UT territory. Austin FC has shown that's not impossible, but still a challenge.
The other option would be to split the difference and set up somewhere like New Braunfels or San Marcos, but then you are asking BOTH people from San Antonio and Austin to drive out and that's a tough sell, too.