Besides the rubrical idea that the GIRM, church documents, and traditions of the church lean strongly towards toward the singing of the propers at Mass, there’s also another important point that is missed in this discussion: important texts of the liturgy are being dropped. When the propers are not sung, it’s almost as if you’re skipping 3 short readings from the Mass (or four, if the tract is to be sung).
For example, take a look at the introit for the Christmas Mass during the Night (ie, midnight Mass).
Ant. The Lord said unto me: You are my Son, today I have begotten you. Vs. Why do the nations conspire, and the peoples plot in vain? They arise, the kings of the earth; princes plot against the LORD and his Anointed. Ask of me and I will give you the nations as your inheritance, and the ends of the earth as your possession.
Translation: Gregorian Missal (ant), Revised Grail Psalter (vs)
Rendered wonderfully by the Westminster Cathedral Choir (this is my favorite chant of all time, by the way):
Now, most parishes this Christmas will probably singing some Christmas carol like O Come All Ye Faithful. There’s nothing bad about that, per se, but it really just covers the whole “Christ is born, let’s all come worship Him” idea. Not that it’s bad, but it’s… a little surface level. Don’t get me wrong: it’s a great carol. But it doesn’t make all of the liturgical connections that we should be making at Christmas.
On the other hand, look at the introit for this Mass. The antiphon is a rarely heard, but reasonably Christmas-themed text: Christ is the son of God, coming to us from heaven in the incarnation. But continue to read on to the verses. We see a clear foretelling and reference of Christ’s passion and resurrection. We’re joyful at Christmas, but at the same time, we must keep things in perspective: this child came here to die a horrendous death for us. It’s certainly not the primary focus of the feast. But at the same time, this is the introit setting the tone for the Mass and the feast. Even in the ancient melody itself, you can hear a reserved joy, but with a touch melancholy hidden there as well.
That’s just one small reason we should be singing the words of God instead of the words of men at Mass.