Short answer: because the rosary was a Western development, and not an Eastern one. The rosary developed as a way for lay people to substitute reciting all 150 psalms; instead, each Ave Maria would represent a psalm. The meditations on the mysteries were a later elaboration, as were the various chaplets that developed (Divine Mercy, etc.).
In the East, what was used instead was the chotki/vervitsa, lestovka, etc., which, like the rosary, started as a simple means of keeping track of short prayers, but never had the accretions that the rosary did in the West.