If you have been "been reading that rail passes in Italy do make much sense. " I'd like to know who suggests that they are a good idea.

You need to make additional purchases of reservations at around 10€ per person per leg on Freccia and IC and EC trains, only the Regional and Regionale Veloce can be boarded without a reservation.

That would be 2 reservation fees for the Lugano to Florence trip (Lugano to Milan, Milan to Florence), then Milan to Naples, and Naples to Rome.

The Amalfi Coast isn't on the train. You can train to Salerno (main line including Frecce) or Sorrento (Circumvesuviana commuter train, passes not accepted).

Passes are not accepted at all on the other high speed train company, Italo, which is a pity because they are an excellent operation.

You can buy very inexpensive advance tickets a few weeks out which may well be not much more money than the pass holder reservation fees let alone the cost of the pass.