That's interesting, JF, though other TP types have expressed grave reservations about the certification/airworthiness requirements of the kind of software that would be required for a reprogrammable-in-the-air FCS, or for specific type simulation, which is what Aermacchi are pushing.
I like the sound of your LP 16 ('different types of handling'), and as a journo and an enthusiastic PPL that's the one I'd like to experience during my famil flight in the M-346 (after LL tailchases and aeros 2), though I can't help but wonder whether it would be, or needs to be, a core part of the syllabus.