We sometimes in my line of work differentiate between a "good aeroplane", and a "good Test Pilots School aeroplane". Sounds like you're describing the latter.
Something with lots of interesting and complex deficiencies that the students can analyse. It's very interesting to analyse the fleets of the various TPSs in that light (or LAA using the Edgley Optica for its flight test courses - now there's a spectactularly good Test Pilot School aeroplane).
I need to go have a go in one sometime (the Tiger Moth, I have flown the Optica, and enjoyed analysing it enormously).
G