We took a cruise with a very similar itinerary (as well as many other cruises) on one of Royal Caribbean's other lines (Celebrity) and it was great!! It is very doubtful you will be able to see Capri and Pompeii and Sorrento all on this one cruise, but you might be able to pull it off. Rick Steve's book on the Mediterranean Port cities might not be a must, but it is a very, very good resource for your trip.
In Athens one of the often overlooked places to go is the ancient Agora which is within walking distance of the Parthenon. Ephesus is well worth the time and effort. If you have a full day in Naples you can do Pompeii in the morning and Herculaneum in the afternoon. Or you could do tour of the Amalfi Coast. In Mykonos a short boat trip out to the island of Delos is well worth doing.
You are correct when you say that the excursions offered by Royal Caribbean aren't cheap. However, we consider them well worth the money because (1) we don't have to worry about the logistics of arranging the transportation from Point A to Point B, (2) we don't have to worry about having the right type and amount of local currency, and (3) we don't have to worry about literally missing the boat. Excursions can (and are) done by many people on their own. And if we plan to just get off the ship and walk about the port we do it on our own. But when it comes to traveling any distance from the ship, we just prefer to leave the cares and worries to someone else so we can just enjoy the excursion.
The problem of being left behind is not just "...a nice scare tactic by the cruise excursions to convince you that you might be left behind...". We have seen folks literally left running down the pier on at least three different occasions. And they did not all happen on the same cruise. Every time we have been in Naples and Athens there have been traffic conditions that prevented us from getting back to the ship on time but the ship did wait. Others were not so fortunate.
On all of the cruise excursions we've taken that included meals the food and ambiance were very good. Nothing mediocre about them at all.
Land touring in Europe and cruising to European ports are two totally different things. Each has its' own pros and cons and it is very difficult (if not impossible) to make direct comparisons. We've done both and thoroughly enjoyed both.
Enjoy your trip.