(beginning with some trepidation...)
Aside from the Freedoms, the other common free standing mast rig is the Junk Rig. First let me say that most people who sail a bermudan (pointy triangle) rig have a gut revulsion
for the junk rig so I know what I'm getting myself into here.
The number one advantage to a freestanding mast is that you can square the main sail straight out at 90* to the boat. There are no shrouds to chafe on or stop the motion of the sail.
Second, as mentioned above, you can't break anything (except your skull) in a surprise jibe. The jibe isn't the problem, it's the sudden stop when the boom hits the shrouds. Otherwise, after a while the sail just dumps the wind and stops.
Although there have been several posts already regarding the potential for breakage on a free standing mast, one can only look at the frequency of dismasting because one measly shroud breaks.
I would disregard any claim that the risk of breaking a free standing mast is higher. Stuff does break, there's no doubt to that.
It is true that, in order to be free standing, the mast must be bigger than a stayed mast. Think of it as the stays being "inside" the mast. On the other hand, it is not necessarily true that the mast adds windage or weight aloft, because stays themselves have windage and weight aloft. (And make a lotta noise.) Add to that spreaders and other hardware, and the difference is debatable and would take considerable wind tunnel research to get a definitive answer. Damfino.
Most junk boats are conversions, because one thing that can't be denied is that the pointy white triangle sells better. It takes a certain kind of hard head to go against conventional thought. There have been, that I know of, three companies that have tried to compete by offering factory junk rigs, and they're all gone now... of course, most of the other sailboat companies that existed in the twentieth century are gone now too, but still, there it is.
Most junk conversions carry about 20% more sail than the original total of the bermudan rig on the same boat, due to ease of reefing and management. This, plus the ability to square the sail right off, gives a hands-down advantage off the wind, unless measured against someone who chooses to use a spinnaker. Typically one will find that the bermudan rig has the advantage on a beat, and a well designed, cambered (to provide lift) junk rig will have the advantage over about 180* from reach through run to the other reach. For more on the cambered junk rig, by a primary developer of the concept, see here
. This makes the junk rig popular among some cruisers, since few cruisers really want to spend a lot of time beating into the wind. On the other hand racers, especially round-the-buoys racers, have no use for it.
The real glory of the junk is in single-handing. One never goes up on the foredeck (except to anchor). There's no sail up there to change. One reefs from the cockpit in five seconds or less with one hand. To tack one just puts the helm over... no jib, no jib sheets. Short tacks are a piece of cake.
I doubt strongly that there is another junk rig aficionado on SailNet. Surely I would have heard from him or her by now.
Two places where one can find more information, and encounter other people who approve of the rig and the free standing mast commonly used with it, are the Junk Rig Association, linked in my sig, and the Yahoo Junkrig Group.