@ Badanov #20
I think the whole FAI/QAI/QWI scheme grew first as a property of the Central Fighter Establishment (CFE) which in the 1950s occupied West Raynham. Our Canberra squadron QAI (1962-65), the excellent late Flt Lt Nev Whittaker, was ex-Hunters and qualified (I think) while still on fighters. I suppose the OCUs collected this post-grad training role when CFE closed 1965 or so. At this stage CTTO had not been invented.
In my time TP was clearly a career cul-de-sac, with the qualification being more valued by foreign air forces and the aviation industry. One in a generation could hope to become Commandant of ETPS.
ASQ has been mentioned. As the successor to SpecN, in my time it held for navigators the kudos of QFI and TP rolled into one - and was a good career move. For a pilot like me it was career suicide !