I am not accustomed to criticise Roman Pontiffs for the contents of their solemn declarations; there are enough people around doing it, most of them Roman Catholics, for it to be unnecessary that Anglicans join in too. But I do have one or two exceptions.
On April 3, 1969, Paul VI signed an Apostolic Constitution (I gather this is one of the most solemn exercises of the papal Magisterium) in which he promulgated the Novus Ordo Ordo Missae. In it he quoted Vatican II : 'elements which have suffered injury through the accidents of history are now restored to the vigour which they had in the days of the holy Fathers.' The third of the items he then listed was 'the Penitential Rite of Reconciliation with God and the brethren, which once more has its due significance'.
Perhaps someone can convince me that this is not a lie. I am not speaking ironically: I honestly do not like to think of a Pope in such a solemn context putting his signature to an untruth. But, as far as my knowledge goes, it is an untruth. In the patristic period Mass did not start with a corporate act of penitence. As I think understand it, the practice of Celebrant and ministers at the foot of the Altar making an act of penitence together, as part of their personal private ministerial preparation for the Mysteries while the Introit is being sung, is a (thoroughly good) medieval addition. It is not patristic; it was not part of the public part of the Mass until the Liturgical Movement popularised the Dialogue Mass. Please tell me if there is something I don't know about.
If, however, things are as I have sketched them, there are practical consequences. If things are as I have sketched them, I would suggest that at sung celebrations of the Novus Ordo Mass the Penitential rite should be done, as happens in the EF, privately by the Altar party under the cover of the entrance music.