PN - Indeed it was - AST.362 was a Gnat/Hunter T7 replacement. Mainly, I suspect, a trainer for TSR.2.
Generally: this trend in T-X reflects the high cost per flight hour of the F-22 and F-35, plus the fact that there are no two-seaters. Clearly one does not want to find out that a pilot is susceptible to high g levels and rapid onset when that individual is alone in an aircraft.
The high cost favors what is called "downloading" or transferring training tasks to a less costly aircraft. A higher-performance trainer does more of this; and since it's an economic case too, if the CPFH on the fighter is high, the economic case will close at a higher CPFH for the trainer.
Also, in addition to undergraduate pilot training (which is what T-X is primarily for) there is growing interest in putting companion aircraft into the operational unit. (ACC resisted this, but now has T-38s on F-22 squadrons.) Budget documents show that this is expressly being taken into account as an adjunct to the T-X program.
What will be interesting is to see what Boeing/Saab and NG propose as clean-sheet designs.
By the way, the Italians are insistent that the requirement does not cut out the M346 - but there's no sign of a partner willing to take them to the dance.