Would this not fall into the category of repetitious prayers?
On the question of repetitious prayers: I spend most of my days wandering around saying "But Thou O Lord art among us and Thy Name is called upon by us, forsake us not, O Lord our God" or some variation of "Lord have mercy on us".
Since the Synod started in Rome I've been practically hammering the rafters with the same constant and very repetitious prayers.
My Protestant father (who now lives with us due to a stroke) says the same collection of phrases at every meal right after the children say their same prayer in unison. Ecumenism is weird when you have to live it in your own home.
So on this business of repetitious prayer, I don't think the variety of phrases assembled matters all that much compared to the Faith being expressed.
The Rosary is much more a meditative prayer; the rote prayers that are used are conducive to meditating on the mysteries. As I said, it is not for everybody, and in my mind it does not take away from the prayer life of those who do not pray the Rosary. I need only look to the wonderful examples of my sister and my daughter. They are both very devout Christians.
Peace,
Rich