Despite the fact that independent tours are usually more interesting, more fun, and substantially less costly than ship-based tours, far too many cruisers who do it on their own encounter challenges that delay the ship
Some broad generalizations here that I do not totally agree with. First, very often independent tours are no more interesting and fun than ship's excursions. Often they cover exactly the same sites (and sights) in exactly the same way. In fact, some of the most fun excursions we have had have been with ship's groups, because the larger group can do more fun things. Check out our trip report and pictures at "Black Sea Cruise 2009"
for our excursion for Zorba dancing at Olympia, for example.
We do frequently book independent excursions. That same page will show you some that we enjoyed. But it is for specific reasons -- sites not covered on ship's tours, special attention to mobility limitations, special shopping opportunities, and so on. I cannot say that generally they are "more interesting and fun." They are often more convenient and more flexible.
Also I really don't think it is true that many passengers on independent excursions encounter difficulties getting back to the ship on time. I think most reputable operators make a huge effort to get back to the ship on time as they know their reputation depends on it. I strongly suspect that those people whose names are called again and again were either on a DIY trip with a taxi driver they met at the dock, or actually far more likely spent too much time in a local bar. It is always fun in Cozumel to watch the last few pax stagger out of Senor Frog's and try to run down the dock. I have also been on cruises where the ship was delayed waiting for a whole bus, or once several buses, to get back from the ship's excursions.
And finally, it has never been our experience that independent excursions are substantially less costly than ship's excursions. Almost all the time we wind up spending MORE for independent excursions. Of course this is partly due to the reasons we book them, and the fact that we book small group independents. Booking an independent excursion that takes a large group to exactly the same place a ship's excursion goes can on occasion (not always) turn out to be less expensive. It can also be true that the ship has booked up the best transportation and guides and an independent tour gets second best.
Again, I suggest balance. Ship's excursions are an excellent starting point and are almost always good, convenient and safe. Independent excursions require more research, and should always be with reputable and recommended guides. Booking a taxi at the dock or trying to DIY on local transportation is for the brave who are willing to accept the small risks involved. And -- spending your time in the local watering holes is not only very little fun IMAO but the most likely to result in safety problems!
So -- the suggestions and warnings usually given by the cruise lines are basically valid. If they go a little overboard in their marketing, so do many of the independent agencies in the other direction. Care, caution, and a risk/benefit analysis are necessary in all life decisions. Which shore excursion to take is not as important as picking a college to go to!