(Thanks to Pr. Paul McCain for this)
The truth is that while we may be “in private” we are never alone when we pray.
First, the Holy Spirit is with us constantly, often providing words and sighs and groans too deep for words, when our words fail, the Holy Spirit strengthens us. Second, the Living Christ and in fact, the Blessed Holy Trinity, is with us in a mysterious indwelling and communion. We are the temple of the Holy Spirit, who never acts as a “free agent” but is always, and ever, with us, in communion with the entire Holy Trinity. Then, there is the mysterious Body of Christ, the holy Christian Church, in which we are constantly in communion, even when we are physically alone. And so, it is entirely appropriate that we pray Matins, even when we are alone, because at all times we are, actually, in truth, never alone. We are always praying with the Church. We are, in Christ, and therefore, where Christ is, there is His body. Here is how Luther put it, very nicely:
Never think that you are kneeling or standing alone, rather think that the whole of Christendom, all devout Christians, are standing there beside you and you are standing among them in a common, united petition, which God cannot disdain. Luther, AE 43:198