Unless someone departing Rome has a flight before 10AM, it's usually better (both experience and comfort wise) to sleep in Rome. You can get so much done from a well-located hotel. Yes. Civitavecchia is a long way from Rome. But car service to Civitavecchia is a widely sold commodity in Rome. Does it cost more than from FCO? I don't know, but it would only be 15% more, at worst. They are still stuck with an empty return that you have to pay for!
Since most cruise ships, economically, have to Turn Around on the same day, 6AM to 5PM or so, you don't have to be there before (can't even board ... ) 1:00PM, likely. There is just no chance of missing the ship if you have breakfast at your hotel, an a one-hour sightsee while the get your luggage downstairs for you. Sometimes when we've had three nights in Rome, the hotel offers a free single transfer, either from/to FCO, or .... wait for it ... Civitavecchia. That's how "important" cruise transfers are to the city of ROME.
Walking ability is not relevant to use of a car service, and the right hotel in Rome could be right by some great sights.
It might not be as easy to get a car service, but Viterbo would be a more interesting place to stay than an airport - but walking is necessary to see it.
https://community.ricksteves.com/travel-forum/italy/rome-airport-to-port-outside-of-rome