There's no way the teams would switch to something like the T-45.
The Thunderbirds once flew the T-38 Talon(Trainer). That aircraft was involved in the team's worst accident (the Diamond crash). At that time, the Air Force practically begged to get the team into a fighter-type aircraft.
The F-16, in my opinion, is the most perfect aircraft for the Thunderbirds to fly. Plenty of power, lots of noise and agility to match most any other aircraft.
Also, you can't forget why these teams exist in the first place--to demonstrate the professionalism of the US Air Force and as an enhancement to recruiting. Flying around in some unimpressive, slow (and ugly) training aircraft would accomplish neither.