Do you find Mediator Dei somewhat repetitive as we move through the document? Pope Pius insists again that lay people cannot advance or even believe the position that private Masses are significantly problematic:
113. We wish in this matter to repeat the remarks which Our predecessor Benedict XIV makes with regard to the definitions of the Council of Trent: “First We must state that none of the faithful can hold that private Masses, in which the priest alone receives holy communion, are therefore unlawful and do not fulfill the idea of the true, perfect and complete unbloody sacrifice instituted by Christ our Lord. For the faithful know quite well, or at least can easily be taught, that the Council of Trent, supported by the doctrine which the uninterrupted tradition of the Church has preserved, condemned the new and false opinion of Luther as opposed to this tradition.”[Encyclical Letter Certiores effecti, November 13, 1742, par. 1] “If anyone shall say that Masses in which the priest only receives communion, are unlawful, and therefore should be abolished, let him be anathema.”[Council of Trent, Sess. 22, can. 8]
I think it is more accurate to say God’s grace is perfect, and potentially works as well with private or public Masses. To a degree, this reflects the supremacy of God’s agency and grace is not determined by human action.
When people participate fully at Mass, however, the sign value is stronger. The gathering and the prayer give the engagement with grace an outward sign. And that may well be important in some circumstances.
114. They, therefore, err from the path of truth who do not want to have Masses celebrated unless the faithful communicate; and those are still more in error who, in holding that it is altogether necessary for the faithful to receive holy communion as well as the priest, put forward the captious argument that here there is question not of a sacrifice merely, but of a sacrifice and a supper of (filial) union, and consider the general communion of all present as the culminating point of the whole celebration.
But the Eucharist is indeed both sacrifice and meal.
And as for the culminating point, this is determined by the twofold purpose of the Mass: the worship of God and the sanctification of the people. When this happens, the culmination occurs. And it can well happen outside of what liturgy as a science will predict, and outside of where one might expect.