Yes, tours (private or cruise line tours) are quite expensive and its actually possible to spend more on tours than on the actual cruise. You ask can one have as much fun without a tour, and my answer after more than 25 years of traveling without tours would be it depends on you. My wife and I dislike almost any tour because we do not like being in a group, herded like cattle, and only seeing what is "appropriate" for tours. We also love to eat in Europe, and our type of long lunches at cute outdoor cafes does not fit into most tours (its possible with private tours). However, to do your own thing in most places requires a lot of homework, some "travel smarts or lots of common sense," a spirit of adventure, and the ability to accept some flexibility in your plans. Everyone of your ports can be done on your own, but for Kusadasi I would strongly recommend that any first-time visitor take a tour (we prefer private over cruise tours). Mykonos, Rhodes, and Santorini can easily be done on your own (but you do need to do your homework). Istanbul can also be done on your own but does require a little more homework. Athens can be done on your own by simply taking the subway line that runs from Pireaus into town (watch out for gypsy pickpockets on this train). When you go to the Acropolis you might want to buy your way onto a local tour or, at least, get the audio tour. Naples really depends on what you want to do since there are so many possibilities. A trip to Capri is easy on your own, but traveling on the Amalfi Drive is best done with a tour or private driver for any first-time visitor. Rome is a sprawling city that can be done on your own by using the train and a decent guide book. But Rome is a challenge because of its size, and some tours can help a visitor avoid the long lines to get into the Vatican Museums (its also possible to pre-book Vatican tours and avoid the long lines).
The two best friends of the independent traveler (we travel like this about 6 months a year) is the Internet and the large book stores like Borders where you can browse books while sipping some coffee at their cafes.