The T-38 really has reached the end of it's useful life. It's been extended several times with structural fixes, avionics upgrades, and even a new ejection seat. But there's only so much you can do to an aircraft designed so long ago that it creates negative training and is unable to prepare student pilots to fly modern aircraft.
I won't fall into the trap of pointing fingers, but it's also reasonable to point out that the mishap and fatality rate of the T-38 is not awesome. That by itself has rarely been enough to justify an entirely new weapon (or training) system in the military but in the case of the T-38, the fact that they knew darn well the airframes were too old contributed to the decision to integrate new ejection seats, a very costly band-aid that let them delay the T-38 replacement program until the F-35 was into production. Run-on sentences were also a consequence.
The T-38 was a great trainer and it remains one of the most fun to fly aircraft I ever flew, but it's utility as diminished well past the point where replacing it is a reasonable cost once you add up all the factors including mishap rate, maintenance costs, and the cost for additional systems that have to make up transition programs before T-38 graduates can effectively train in modern aircraft. Every single sortie off-loaded from F-35 upgrade training down to the advanced UPT syllabus probably saves $10,000 or more. That adds up bigly.
