Some of this is natural.
There were plenty of empty seats in the 17,000 seat arena in Austin, too. Same thing happens yearly at the Big Ten tourney, which is far more regional. I don't think regional sites would help all that much.
Part of the issue is whenver you have several schools involved, many fans only are interested in their own school. So, when Michigan is playing Kansas, the arena has all of the Michigan and Kansas fans, but only part of the Florida and Florida Gulf fans are. And, vice versa.
In addition, the reason some of these regionals are in football stadiums is because they use those as a test run for future Final Fours (i.e. Arlington this year for regionals and next year as Final Four).
No matter, we will never see again a Final Four in an arena, so the football stadiums will continue to host Final Fours (and because of that, also regionals).