I have seen demonstrations of medieval Japanese horse archery in which the archer is shooting with his grip on the bottom 1/3 of the bow.
If the Japanese only developed one type of bow this would make sense because you can't use a longbow from horseback by gripping it in the middle. Being a Samurai was expected to be an all around warrior it would make sense that he would carry only one type of bow for both types of combat.
Armies that were horse based developed the horse bow specifically to allow the archer to fire from horse back. Armies that were more infantry based (and culturally more homogeneous) tended to go for longer bows even it it wasn't a true long bow.
kisses
willowfall