Saint Dominic was meditating on the life of the Lord Jesus. He also intended to honor the Virgin Mary, in the FRAMEWORK of the major EVENTS of the Savior's life. The Saint thought of the "Rosary" as a crown of roses on the head of the heavenly Queen.
At the time where the PSALTER was well memorized by many people, Saint Dominic thought of the illiterate. For such people in particular, and for the Faithful in general, the 150 "Hail Marys" were meant to remind of the 150 Psalms.
The Rosary - in Arabic- "missbahah", "praise tool" , is NOT at all meant to "praise the Virgin, as if she were a goddess", but to praise THE LORD through and with Mary who had sung :"My soul praises the LORD and my spirit rejoices in God my Savior". As a matter of fact, the "Hail Marys" are preceded by the Lord's Prayer ("Our Father") and always followed by the "GLORY" - not to Mary - but to the Trine One God.
The muslim world has also a "misbahah", for the praise of Allah, with 33 beans- which , multiplied by three, reach the number of 99, the traditional "best names of Allah" (al-assmaa' al-hussna) الاسماء الحسنى
When Greece was threatened by the Turks, the Italian navigators prayed the Rosary, back in 1571. To Our Lady they attributed the Lepant (today Navpaktos) victory - recalled every day three times at the Angelus bells. That was on October 7, 1571, later insalled by the Pope as the feast of "Our Lady of victory" and later "Our Lady of the Rosary".
This is an opportunity to clarify that the Church never worshipped - nor taught to worship the Virgin Mary as a goddess. One might find here and there some exaggerations in popular devotion, contrary not only to the Scriptures but also to the Church directives. Mary is "the Mother of the Lord" (as acknowledged by her relative Elizabeth) but NOT the Lord.
As for the repetition of the Hail Marys, it is not meant - like the heathens - to awake a sleeping god but rather to express love and respect, veneration to Mary not adoration. The Lord Himself repeated the same prayer thrice at Gethsemani. The Psalm 136 (135 according to the Greek) repeats "Because eternal is His love (or mercy)" 26 times.
When Bishop Fulton Sheen was asked by a young fiance' :"Why do we repeat so often the Hail Mary?" The Bishop asked :"How many times did you tell your fiancee that you love(d) her?"
Let us not forget that the Rosary is a popular prayer, not the official one which we find in the Holy Mass and in the Breviary.