Pope Pius XII notes that as the faithful offer sacrifice, it is not considered a liturgical rite. Not a visible one, anyway:
93. Now it is clear that the faithful offer the sacrifice by the hands of the priest from the fact that the minister at the altar, in offering a sacrifice in the name of all His members, represents Christ, the Head of the Mystical Body. Hence the whole Church can rightly be said to offer up the victim through Christ. But the conclusion that the people offer the sacrifice with the priest himself is not based on the fact that, being members of the Church no less than the priest himself, they perform a visible liturgical rite; for this is the privilege only of the minister who has been divinely appointed to this office: rather it is based on the fact that the people unite their hearts in praise, impetration, expiation and thanksgiving with prayers or intention of the priest, even of the High Priest himself, so that in the one and same offering of the victim and according to a visible sacerdotal rite, they may be presented to God the Father. It is obviously necessary that the external sacrificial rite should, of its very nature, signify the internal worship of the heart. Now the sacrifice of the New Law signifies that supreme worship by which the principal Offerer himself, who is Christ, and, in union with Him and through Him, all the members of the Mystical Body pay God the honor and reverence that are due to Him.
Lay people are united with both the ordained priest and the divine priest. The other principle described here is that external ritual “signifies” an internal worship. Clearly, the notion of interior participation and exterior ritual is one of either/or, something in conflict or part of a zero-sum spirituality. The two aspects are linked deeply. One signifies the other. Each contributes to the other.
Pope Pius is concerned about things getting out of control:
94. We are very pleased to learn that this teaching, thanks to a more intense study of the liturgy on the part of many, especially in recent years, has been given full recognition. We must, however, deeply deplore certain exaggerations and over-statements which are not in agreement with the true teaching of the Church.