There are many aspects of liturgical prayer that are absent in that mode of prayer that involve the body. For instance, the normal posture for liturgical prayer is standing. In the Benedictine tradition one stands during much of the office, although one sits on a perch in one's stall during the recitation of the psalms. One bows at the "Gloria Patri" and makes the sign of the cross at the Gospel Canticle.
Usually in liturgical we face the altar or some image of the Lord (a crucifix, for instance). Normally we are in an oratory. Since we can't all go to Church, many of us have an oratory set up in our "domestic churches." That might be an appropriate place to pray the office. In the recent movie about the Carthusians, Into Great Silence, that the monks prayed kneeling in a private oratory in their rooms facing a crucifix. I at least face an image of the Sacred Heart (the same one that is to the left on my blog), although I'm still sitting in a comfy chair.
The other thing that a silent or whispered recitation abstracts from the "normal" celebration of the Office is music. The psalms are meant to be sung. When we just sit there and "pray" with our minds, we are not involving the body at all. When we just whisper we may be involving the body (the lips), but we aren't involving the body as it is meant to pray--with music.
Finally, the Office is the consummate corporate act of worship: it is meant to be prayed in a group. I know the private recitation developed in order to make missionary activity easier, but one wonders whether efficiency ought to be the only criterion for missionary activity. I mean, what might have been the missionary effect if the missionaries had traveled in groups and sung the office together. They may not have been as mobile or gone as far, but the very witness of the Body of Christ in worship may have had a deeper affect than simply proclaiming the Word with a purely private and hidden piety.
One of my criticisms of the Jesuits is their tendency to interiorize their spiritual life so much that there is no obvious manifestation of their devotion to God in their bodily life beyond Mass (which is itself often celebrated in a cerebral way). Ignatius' decision to allow private recitation of the office rather than corporate may have allowed for missionary mobility, but did we pay a price in a sense of the bodily and corporate nature of Christian worship? Might a more bodily spirituality have make some Jesuits more open to and receptive of John Paul II's theology of the body?