I was at a party about 10 years ago and got to talking to an elderly American gentleman. He was a retired USAF fighter pilot and somehow the topic got on to flying instructing. I asked him if he had done an instructor tour during his time in the Air Force.
His response was no, he had never been selected for an IP tour although he had asked for one as his last pre retirement posting. He figured that the powers that be, must have thought him unsuitable as he had flown operationally in WW 2, Korea, and Vietnam, and been shot down in all three wars !