As far as I know, there are only two styles of taiko in Japan which are based on improvisation: Fukui/Hokuriku style and Hachijo style, both styles simply named for the places they’re found.
In Fukui style pieces, improvisation can takes place within a pre-determined structure, such as a song which has elements of unison and chances for individual players to play solos. One can also improvise based on an informal structure (such as when playing a duet, ‘futari uchi’) or completely freely.
My teacher, the late taiko master Kurumaya-sensei, observed that if one never improvises on stage (e.g. playing a pre-composed solo instead of an improvised one), then one’s solo may never be terrible but will never be great. In other words, if you always play it safe, you won’t experience those times when it all just comes together and you play something new and beautiful and surprise yourself.
It’s also good practice for life.
Improvisation is one way to work. For some, in some instances, it brings freedom: the freedom to follow impulse and the intelligence of the moment, the freedom to arrive at the right parameters for the structure of that moment without binding it with formality, the freedom to work at the speed of a thinking body and mind.
— Jonathan Burrows, A Choreographer’s Handbook, thanks to Collective Endeavours for the reference