Given that, at that time, there would have been no huge difference in performance between trainer and operational types, would there even have BEEN dedicated Pup (or Nieuport, or SPAD) "training" (either IJN or IJA) units? Might the "on Type" training simply have been left to the operational units? Also, given the relative size (numbers & budget) of peacetime Japanese (and every other nation's 1920's, for that matter) air arms, would it have made fiscal sense to maintain front-line types in dedicated training units?
Dunno, but you asked for thoughts. . .
Regards, Rob