We first did this in December 2012, so it’s been some time, but we rented at the Palermo Airport with Europcar and headed immediately west, first for the remarkable Greek temple at Segesta, then on to Erice, Agrigento, Caltagerona, Piazza Armerina, Modica, Siracusa, etc. The rest of the passengers on our flight from Rome to Palermo were all speaking German, and all went to the Sixt desk upon arrival. Europcar gave us a great car at a lower price. Nobody, though, was counting on public transportation, and you noted the benefits of flexibility and luggage management, and I’ll add going on your own schedule, where you want to go, and in what order. We turned in the car at a different location, actually on mainland Italy, after taking it across on a ferry at Messina, so a round trip isn’t required, unless that’s how you’re going to do it.
Six years later, a former teaching colleague and I stayed in Palermo for a few days, then rented a car to explore farther south, then east. Again, we weren’t tied to train (or bus?) routes or timing. Parking and getting gas were part of the car rental process, but not a hassle, given the benefits.