Splitting the difference based on population makes sense mathematically, but I think a "middle ground" location would just alienate both major metros.
Personally, I can attest that since I moved to Austin, I go to far fewer games. I don't really mind the drive, but it's a much bigger commitment for me to drive 2 hours each way from north Austin (usually during high traffic times) for a game then it used to be when I had to drive 20 minutes. That definitely factors in to my decision making, which is why I only go to one or two games a season these days and its usually a planned event (i.e. seeing family in San Antonio, getting a hotel downtown, etc.)
If they were to move to, say...New Braunfels, you are asking both the San Antonio and Austin folk to commit to at least an 45 minutes drive just to get to the arena. Season ticket sales would suffer, and overall, people would be far less inclined to go to a game on a whim.
Couple that with the fact that San Antonio has a longstanding history being....well, the San Antonio Spurs, and they won five championships there...that's sure to rub some of the old-timers the wrong way. The Spurs are synonymous with San Antonio at this point, and if they were to become the Austin Spurs (or even the South Texas Spurs or whatever)...a lot of people are just going to stop caring as much.
Like others have said, the cost of building an arena in the heart of Austin would be astronomical and Travis county probably wouldn't even go for...plus there is just not really room to build. So they would be left looking on the outskirts either way, whether that is Buda, Cedar Park, Round Rock, etc. But I don't see a real benefit of moving the team 100 miles up the road from its historical home.
I think the Spurs will continue to be the San Antonio Spurs for a long time, but if they do move....it's probably going to be far away.