The only time mizzen is used by itself
I have limited experience sailing with a mizzen, but the only time I have ever seen or heard of using a mizzen alone is while at anchor; it will act as a windvane keeping the boat pointed into the wind. Actually sailing with the mizzen alone? I would think that the biggest effect would be to create extreme weather helm as the sail would try and shove the stern to weather (and pointing the bow into the wind), requiring a lot of effort to stay on course. The big advantage to the ketch and yawl rigs is that the additional sails allows for each sail to be smaller and therefore more manageable; it also allows for a greater number of sail combinations (jib and main alone while working to windward, all three sails on a reach, jib and mizzen alone in heavy weather, etc.) allowing the crew to get the most out of the boat. The conventional wisdom is that the ketch/yawl rigs really shine on reaches when all the sails can be used, and in heavy weather when you can douse the main entirely and still stay balanced by using the jib and mizzen. However, it seems to be a given that the rigs are not nearly as handy going to weather as a sloop. The mizzen takes sail area away from where it would do the most good in those situations (the jib and main). The rigs seem to have also lost some of their luster in recent years as better sail handling equipment has come on the market. Cruisers used to covet the smaller sails which made them easier to handle in a blow; however with the development of reliable in-mast and in-boom main furling systems and the continued development of jib roller furling, the larger sails of the sloop are no longer as hard to handle for a cruising couple. Less hardware and rigging to maintain, less deck clutter, fewer sails to buy, more room in the cockpit. For my money however, ketches and yawls sure look salty. Yarrr.