I'm not sure why they don't consider US 281 up to just SW of the Metroplex for such a project. It would solve several road congestion problems, as well as providing a much needed link to the great Austin area to SA and a more direct route to the Metroplex from the south...
Likely because it is much further away from Austin, so it would be a good bit more indirect and with fewer users. Also the terrain is more hilly, increasing the construction costs. Getting around the San Antonio metro would add more mileage, and would be tougher to do on the more rugged west side. But 281 is going to be upgraded to 4-lane the entire way. Not sure the timeline, but remember reading that somewhere.