The Rosary repetitions are not meaningless rote, they are devotional, and the Rosary also is about reflecting and meditating on the various Mysteries, and the fruit of each Mystery. For example, traditionally on Monday one says the Joyful Mysteries; the first being the Annunciation-
The angel said to Mary, "You shall conceive and bear a son and give him the name of Jesus. And he will be called Son of the Most High." Luke 1:31-32
The second is the Visitation, then the Birth of Jesus, the Presentation (in the Temple), and Finding the Child Jesus in the Temple. The respective Fruits being Humility, Love of Neighbor, Poverty, Obedience, and Joy in finding Jesus.
What a wonderful way to pray :)
I fail to see any scriptual references to any of these. These appear to be manufactured 'mysteries'; not biblical, but an effigy derived from the bible. Isn't the purpose of the Rosary a means of 'keeping score' on how many times you have repeated a set prayer? Again, I see nothing regarding this in the Old or New Testament.
Consider: Mark 7:7 - Howbeit in vain do they worship me, teaching [for] doctrines the commandments of men.