There is no excuse for this shameful waste of valuable assets.
Here is a little more info and interesting comments at this site:
http://aeroweb.brooklyn.cuny.edu/specs/slingsby/t-3a.htm
The engine would be repeatedly started and stopped (they are trainers). During the summer, the engine would vapor lock. The T-3's engine had failed 66 times at takeoff or landing (pressure and temp differential and changes in manifold pressure possible exacerbated by altitude).
What would prevent it from happening in the air? It probably did during the three fatal crashes although two were attributed to pilot error and one to an "out of envelope" excursion.
The predecessor T-41 had no fatal accidents in 30 years of flight, it just wasn't as aerobatic.
Of course, we're talking about the same bunch of AETC clowns that took a great fleet of T-38s and nickel-and-dimed them into something downright dangerous.
Sell 'em. Then someone will get injured and sue. This just just another bunch of lawyers looking for income.
Flight screening does a good job of weeding out folks who have no business going to Air Force pilot training. Back then, everyone went to the T-37 and then the T-38. It is expensive to send a student pilot through that program, only to learn you have to wash them out after weeks or even months.
The C-172 did a good job, but some people complained that you needed an aerobatic trainer in order to separate out folks who would get airsick, or who just couldn't handle the demanding regiment of AF pilot training. Acrobatics is hard work - energy management isn't easy, and thinking in 3-D while flying a jet isn't for everyone.
The problem was the T-3 was, and is, a pig. And a dangerous one.
They should have just purchased more C-172s and left it up to instructors in the T-37 to "make the call" early if students couldn't handle Air Force flying.