The cavalry busha was not a specific right of medieval bushi, but a tradition of having cavalry with archers as the main military force that continued uniformly throughout from the cohort of the Ritsuryo system to medieval bushi.
騎馬武者は中世武士の専売特許ではなくて、弓射騎兵が武力の中心という伝統は律令軍団から中世武士までの一貫したスタイルである。