I always carry my pp, but the "average" tourist (from USA, say) might not be aware of the RULES--many probably leave them in their hotel rooms [US pps are relatively bulky!]
Re ID, would they accept a US Drivers license, pp CARD, GE (Global Entry) card?
This is not about being aware of the RULES but being aware of where the BORDERS are. Anyway I suspect the reaction of Swiss/Italian authorities would not be as extreme as what happened to this
French citizen.