I attended Mass in Las Vegas, at the Cathedral there, and they did just that. It was nice.
At Holy Family Church in Hilton Head Island, SC, before Mass began the celebrant would ask everyone to stand & introduce themselves to those around them with names, hometowns since most were visitors, & handshakes that were far more genuine than the mid-Mass SOP.
In 1975 I joined a parish which had a pastor who omitted the SOP. After Mass I asked him why (approvingly), and this tough old priest replied, “Look, son, I’m the celebrant. When I say `the peace of the Lord be with you all’, that’s all there is, there isn’t any more!”
Nowadays after the SOP, everyone breaks out the Purell. Years ago we got home after Mass & washed our hands thoroughly. SOP sucked then and does now. Sixties leftover touchy-feely stuff, like guitars & tambourines.
Slyfox:
I have always thought it should be before the penitential Rite. Have the same Rite of Sign of peace and then move into the Penitential Rite.
In Miami it's pretty over the top.