Why would UT have a tough time winning at baseball? I'm an LSU fan, but always had a soft spot for Tenn as I grew up in Chattanooga.
Anyways, UT has decent facilities (not as important in baseball as football), it's a public school (helps to have cheaper tuition since baseball only has 11.7 schollies), and Tennessee has decent in-state talent (much better baseball talent than football talent in state) and is close enough to GA, OH, SC, and NC to recruit good out of state talent.
The main competition in-state is Vandy. If Tenn can show they can win, they'll easily win the recruiting battles because many players would much rather afford the Tennessee tuition than the Vandy tuititon. Tennessee has a lottery scholarship that can help with some players which means those schollies can be spent on out of state players. That's an advantage that programs like Bama, Auburn, Ole Miss, Miss State, Vandy (due to high tuition) and Missouri don't have.
Just because Serrano doesn't win here, doesn't mean nobody can win here. Delmonico won here and he was kinda lazy.