One of the hidden benefits to a common orientation of priests and people towards the Lord in liturgy is that the priest is free to pray. Instead of having to compose his face for public viewing, he can be himself before His God. He can return to honesty and simplicity. He has a unique role, surely, but it is a humble role. He is not the central focus of the action, like an actor, but its true servant.
Similarly, the people of God can pray to God without meeting the eyes of the priest. They can be honestly praying the prayers to God, instead of composing themselves to be seen as respectable before the priest. The Mass is a time for honesty and clear intentions, not for show. "Your life is hidden with Christ in God."
The priest is indeed an intermediary in the Mass, but it is "no longer I, but Christ in me."
Although we are together, let us take our eyes off of one anothers' eyes, and let each other pray.