Does praying the rosary violate Jesus' command to not "heap up empty phrases" and "many words" (Matt. 6:7)?
If the rosary were simply about repeating words, then it would violate Christ's. However, the rosary is about meditation. When we pray the rosary, we are saying the prayers while meditating on salvation history.
The rosary is not magic or superstition. We do not simply say X number of Haily Mary's and X number of Our Fathers and X number of Glory Be's, and, voilà, our wishes come true. Praying the rosary is about meditating on the events of salvation history and what God reveals to us through them. It's no different than praying and meditating upon the Psalms or certain passages of Scripture.
Jesus himself repeated prayers:
He advanced a little and fell prostrate in prayer, saying, “My Father, if it is possible, let this cup pass from me; yet, not as I will, but as you will.”
Withdrawing a second time, he prayed again, “My Father, if it is not possible that this cup pass without my drinking it, your will be done!”
He left them and withdrew again and prayed a third time, saying the same thing again
(Matt. 26:39, 42, 44).
To claim that simply repeating the same prayer is a violation of Jesus' teaching would be to claim Jesus violated his own teaching!
Are the angels in heaven violating Jesus' teaching by praying the same prayer forever?
The four living creatures, each of them with six wings, were covered with eyes inside and out. Day and night they do not stop exclaiming: “Holy, holy, holy is the Lord God almighty, who was, and who is, and who is to come” (Rev. 4:8).
Jesus' point in Matthew 6:5-8 is about prayer without heart, prayer without soul, prayer without inner meaning. Jesus is condemning superstitious prayer that thinks the right combination of words will produce a desired result. Praying the rosary is about mediation and worship of God, not finding the right formula to get what we want.