Sealed With a Kiss

Adoremus Magazine has the USCCB's CDW's explanatory note about the Circular Letter  from its Vatican counterpart trying to rein in the silliness that pervades the exchange of peace at too many parishes.
The history is interesting to me.
Full disclosure, my current parish generally omits the Peace, but it is in the interest of shaving 15 seconds off the time the pastor spends in church rather than for any theological or liturgical leanings.
Fuller disclosure, I HAAAAAAAAAAAAAAATE the Exchange of Peace, but again, not for any actual theological or liturgical reasons, but for the circus it has almost always been in my experience. If every place performed the gesture with the attitude I experienced at a monastery, once, and once only, I would be leading the charge to get my pastor to instate the practice, with proper catechesis.
But the level of reverence and the depth of religious fervour and the gist of most vocalization by the participants is about the same as all those things as they are performed at the K of C Pancake Breakfast that might follow.
There is no religious ritual enacted, there is no prayer being made
School Mass, IME, are the worst, but Sundays, when the ritual dialogue is likely to be, Hey, how are ya? see you at the scramble next Saturday, got a foursome already? is not much better.

But apart from its typical practice, what is the reason it is so despised by those who line up on the more formal side of the liturgical and cultural divide?
And apart from the chance to stick it to those people, what is the reason it is so championed by those who line up on the other side of the liturgical and cultural divide?

It strikes me as so much in political conflict does, positions chosen to maintain party lines, not for any real principle. (Else, why would you have people who think the government impinges on ones freedom by regulating business practices, but not by regulating sexual practices? And vice versa?)

There're a lot of cases of, Well, if HE likes it, I'm ag'in' it! going around.

Sometimes, the same seems to go for the placement of the Pax - there is one school of progressive liturgical thought that seems to despise any practice in which the Latin Church might be like Her more So this caught my eye:

Among early Christians (e.g., Tertullian), the kiss of peace was seen as a seal placed on prayer. This gesture became a stable element of the liturgies of the early Christian world, including in the city of Rome. At Rome, it may have initially occurred after the Prayer of the Faithful which concluded the Lit-urgy of the Word. In such a position, the kiss of peace was viewed as a sign of mutual love before offering sacrifice (Mt 5:23-24). The Eastern liturgical families retained this placement and adopted this perspective.
For reasons not entirely clear to liturgical scholars, the exchange of peace in the Roman Rite developed along different lines and with a different theological emphasis. In North Africa, Saint Augustine was already familiar with the practice of exchanging peace after the Eucharistic Prayer. In a letter written in the year 416, Pope Saint Innocent I, responding to a list of liturgical queries from Bishop Decentius of Gubbio, writes that in the Roman liturgy, the only proper moment for the exchange of peace is after the Eucharistic Prayer and before Communion. Instead of the emphasis on reconciliation as found in the Eastern liturgies, St. Innocent justifies this placement as an expression of the assembly’s consent to what the priest has just prayed in the Eucharistic Prayer, and the community’s “seal” on the priest’s sacred actions — an embodied extension of the Great Amen (cf. Epistola 25 Decentio Augubino 1, 4).

(Speaking of Adoremus, r.i.p., Helen Hull Hitchcock, what an enormous, enormous service she performed for the Church in America. May the Lord reward her!)