Giving to God what belongs to God
“So each of us shall give an account of himself to God.” Romans 14: 12
"Obey your leaders and submit to them; for they are keeping watch over your souls, as men who will have to give account.” Hebrews 13: 17
Hail Mary & Prayer of the Faithful
The Prayer of the Faithful is to be concluded by the Priest as presider, in the person of Christ, addressing an oration, or formal prayer, to God. Since the prayer is in a sense, Christ addressing God, replacing the oration with a communal recitation of a prayer to Mary or any Saint misses the point of this part of the Mass. Our Lady would want us to be humble and obedient.
GIRM 71 says,"It is for the Priest Celebrant to regulate this prayer [of the Faithful] from the chair. He himself begins it with a brief introduction, by which he calls upon the faithful to pray, and likewise he concludes it with an oration." ​An oration is a formal, liturgical prayer offered by the Priest Celebrant. (See Fr. John Hardon's definition of "oration" at Catholic Culture.)
GIRM 30 states: "Among those things assigned to the Priest, the prime place is occupied by the Eucharistic Prayer, which is the high point of the whole celebration. Next are the orations, that is to say, the Collect, the Prayer over the Offerings, and the Prayer after Communion. These prayers are addressed to God by the Priest who presides over the assembly in the person of Christ, in the name of the entire holy people and of all present. Hence they are rightly called the “presidential prayers.""
GIRM 32 states: "The nature of the “presidential” parts requires that they be spoken in a loud and clear voice and that everyone listen to them attentively. Therefore, while the Priest is pronouncing them, there should be no other prayers or singing, and the organ or other musical instruments should be silent."
Some places in the world traditionally include a Hail Mary in the Prayer of the Faithful. However, according to some of the articles posted below, this practice has been discouraged by the Vatican. To find out more about what is approved in your area, you would need to refer to your Bishop or Bishops' Conference.
For more discussion of this topic, see the following articles:
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"Bishop urges priests to drop the Hail Mary from Masses" In this article from 2012, the Bishop makes a distinction between liturgical prayer and devotion. https://catholicherald.co.uk/bishop-urges-priests-to-drop-the-hail-mary-from-masses/
"Concluding the Prayers of the Faithful" by Fr. Edward McNamara. Father points out that, "This prayer [ending the Prayer of the Faithful] is said with hands extended as for the other presidential prayers." https://www.ewtn.com/catholicism/library/concluding-the-prayers-of-the-faithful-4292
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"Q: It is appropriate to conclude the Universal Prayer with a prayer said by all, such as the Hail Mary or other text?" by Father Eusebius Martis. In this article from 2018, Father quotes the USCCB Newsletter: "The priest celebrant offers the “concluding prayer, which should always be brief, [and] is always addressed to God the Father…,” since the liturgical prayer of Christ’s body is always joined to the prayer of Christ the Head who prays to his Father (Bishops’ Committee on the Liturgy Newsletter, 11:3, 468)."
https://adoremus.org/2018/09/q-appropriate-conclude-universal-prayer-prayer-said-hail-mary-text/
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"A Hail Mary at the End of General Intercessions" answered by Fr. Edward McNamara. In this article on ePriest from 2021, Father quotes the guidelines of an English diocese. The quote begins: "The Roman Rite does not envisage the inclusion of devotional prayers in the Prayer of the Faithful since, as a set of prayers directed to the Father, through the Son and in the power of the Holy Spirit, it contains no obvious place for prayers to the Saints. The Holy See has discouraged such additional prayers." https://epriest.com/liturgies/view/2253