But the deeper reason for why passing the peace is a better liturgy than the "let's stand and greet those around you" liturgy is that passing the peace focuses us on the true foundation of Christian community.
The problem with the "greeting time" liturgy is that it asks us, in sixty awkward seconds, to find some common ground between yourself and a stranger. You ask those standard get-to-know you questions, looking for some point of connection.
The theological issue here, beyond this time being hell on introverts, is that this "greeting time" liturgy is forcing us to look for the source of community within ourselves. We look for commonalities and similarities, and when we find these we find connection and community.
In short, the "greeting time" liturgy is malforming us as it is asking us to find community in similarity and sameness.
Passing the peace, by contrast, points us away from ourselves toward the true ground of Christian community: the peace of Christ. We don't bond over the fact that we both watched the Dallas Cowboy game. We bond because we are recipients of the peace of Christ.
The "greeting time" liturgy is awful because it brings up college football.
Passing the peace, by contrast, points us to Jesus.