There was an odd parallel between your simulator run in a T-38 to how the Army trained fixed wing pilots back in the '60s. (I told you I was old!)
This was before the Air Force made the Army give up everything with wings (with some exceptions). Fixed wing students trained at Fort Rucker on the O-1 Birddog, but they did their instrument training in T-55 Barons, which they were not checked out in.
I'm sure the IPs made sure each student had some experience in all aspects of operating the aircraft, out of self-preservation, if nothing else. But the intent was to provide instrument training in a properly equipped aircraft that could carry an IP and two or three students.
I can think of several reasons why that approach made sense, like having the non-flying students watch and learn from the mistakes of others, and maybe instrument instruction is easier if the IP and student are seated side-by-side. This was before the days of sophisticated simulators.
It's also probable that the Army could justify the purchase of twin-engine civilian aircraft without incurring the wrath of the Air Force. Asking for T-28s or T-34s might have raised the red flag for the guys in blue.
Sorry. I tend to wander away from the subject at times. I'm full of old stories . . . and full of other organic material, according to my wife.