The City of Austin would never finance a baseball stadium. It almost happened at the AAA level 25 years ago when the Giants agreed to finance 40% of a stadium in a part of town that could have benefited from the investment, but the locals cried "foul!"
We did just come to an arrangement for a new MLS soccer stadium, privately financed on city-owned land, but with 20,000 seats.
The 2 million folks around here have a whole lot of ways to dispose of their entertainment dollars, and I'm not sure how MLB would fare.