In my parish it is sung with verses what you posted and also benedicts gals “in heaven the blessed” (but with “fair name”) and two or three more **
It’s the de facto hymn in my church for all Marian feasts, rosaries and Benediction in May and October, any other solemn rosaries, and Marian song at the end of the Mass and often the Mass at the weekly novena.
Personally, I groan a bit because I hear it so much and my parish loves to drag out the last syllable in the slowest possible manner. But all that aside, it is an expression of devotion and I should probably be happy that they’re singing that instead of something else instead of being a grouch. Though I would much prefer one of the Gregorian chant antiphons like Ave Regina Caelorum or Salve Regina.
** (For poor, sick, afflicted, thy mercy we crave, and comfort the dying though light of the grave.
In grief and temptation, in joy or in pain, we’ll ask thee our Mother nor seek thee in vain.
In death’s solemn moment, our Mother be nigh, and as children of Jesus O teach us to die
There are one or two more but I can’t remember them because they’re rarely sung- - they usually stop after 4 or 5 verses when the priest leaves the sanctuary. One is about heaven and light, and something about angels and the Queen I think . I should look in the hymn book if I can find one. )