These days many Catholics don't get to experience the beauty of nine fold Kyrie and appreciate it on most Sunday Masses. When Kyrie is sung after the absolution, it seems to have more distinctive role and form as an Ordinary part, like Sanctus, Agnus Dei.
After I learned to sing Gregorian chant, I discovered nine fold Kyire. (since my parish never did it.) I taught it to my children's schola, and they have been singing nine fold Kyrie for last four years. I explained to them about how we take time to ask for His mercy, especially before we receive our Lord in the Holy Eucharist, as well as about nine choirs of Angels. Although the children were somewhat confused at the beginning, like anything new, they learned that they have to be actually alert and engaged in singing it nine times (alternating between boys and girls.) And now they get very disappointed if we have to sing only 6 fold.
Although in the early church when the liturgy is not yet organized and many things were going through various changes and tried out, chanting Kyrie in the traditional Mass of the Roman rite that we have inherited is done in nine fold. Maybe nine fold Kyrie helps us to remember that we cling on to God's mercy and its beauty, especially in time where 'the sense of sin' has been lost and depending on God's mercy.
Since the new GIRM seems to encourage nine fold Kyrie more than before, maybe parishes can do 6 fold during Ordinary time and progamm nine fold Kyrie at least during Lent and Advent, (since Gloria is not sung during those seasons, the extended time may not be the issue. And since we do extra good things during Lent, and it is encouraged to continue them even after the Lent, the spirit of nine fold can be carried to 6 fold in Ordinary time and appreciated it in a deeper manner.), and have polyphonic settings for major feast days?