Regarding the recent Mass in Edmonton, Fr McDonald laments the lack of chanted Propers. In fact the lectionary Propers (Responsorial Psalm and so-called Gospel acclamation) were chanted. There are no prescribed melodies for these, and some settings can verge on the operatic. This is particularly noticeable, to English ears at least, in St Peter's where the RP is rendered in Italian by a cantor who sees himself as a reincarnation of Pavarotti.
The Introits and Communions given in the Missal are not designed to be sung. Of course the optimal choice would be the Propers from the 1974 Graduale (Introit, Gradual, Alleluia/Tract, Offertory, Communion) and whereas they would suit a Solemn Latin Mass, they would seem anomalous in a celebration where even the sung Ordinary is in the vernacular and in a popular up-beat style. They require considerable skill in execution, and how many modern pew-sitters would opt to sit through a long melismatic Gradual, even when provided with a translation? After all, they have had nigh on sixty years of dumbed-down liturgy whose musical content would make an advertising jingle seem like high art.