I've rented from Hertz in Rome - but not at FCO itself. Due to the supposed craziness of in-city Rome driving (and expensive parking), we actually rented from a Local Edition that was right near the Marriott Grand Flora hotel. We were doing 2 days in Rome (where you really don't need a car in the downtown area) & then roadtripping through Tuscany, the Alps, down to Nice & Monoaco & returning the car at FCO - which there was no additional charge to do.
It worked out much better (for us) and the only problem we had was figuring out how to return the car. When we got to FCO, we couldn't figure out how to open the liftgate that allowed us entrance to the parking lot. We got there before the Hertz location was open (or there were just no attendees there), so depending on what time your flight out is (if its an early AM flight), I'd recommend giving yourself a little extra time. We ended up tracking down a Hertz employee in the airport itself, but it took us another 30 minutes. There were two other US renters that were just as confused as how to enter the lot as we were. Maybe we were morons - but it was an overall pain in the neck...
Regarding cost savings - yes, you do have to get the LDW - it's not optional in Italy - also, I normally use Amex, but for this particular rental, I remember Visa having coverage in Italy (acting as primary insurance) and Amex not - so you may want to check on that. I used the Travel Partners CDP & got a good rate - the other option we were considering was using an Avis CDP - but it equaled the same price as Hertz & I prefer Hertz.