The right way to view the pros and cons is to understand the basic mechanics of how a sailboat works, so you can decide what's appropriate for your situation.
The first thing to be aware of is that unless you only ever sail straight downwind, then sails don't work like parachutes, they work like airplane wings. The motion of the air over the shape of the sail generates a force which can be used to propel the boat. In addition to that force generated, the air generates two forces that must be resisted: the force of the wind trying to blow the sail over and heel or capsize the boat, and the force to push the boat sideways.
Resisting the sidways force is addressed in most boats with a hydrodynamic element called a keel, which shares the same name as the structural element of the boat, and includes weighted keels, centerboards, daggarboards, leeboards, and others. Leeboards are popular with sailing canoes, because they don't requite much if any special built provisions in the canoe, and they don't increase the draft of the boat.
Resisting the heeling force is usually handled by ballasting the boat, either lead in a fin keel, water ballast in trailerable weekender type sailboats, or the body mass of the crew on smaller boats. On many small racing sailboats, the crew of the boat hangs out off the edge of the windward side to balance the powerful force of the air on the sails. As canoes are not really meant to handle sideways loads and can easily tip, this makes an outrigger of some sort usually necessary.
Now, you could make an outrigger to address both those forces, by designing one with a shape to resist the lateral motion. This can work, and there are boats that have that, such as a Hobie 16 which has no daggerboards and instead has asymmetric hulls, but there are some trade-offs. The shape has a less than ideal cross section for buoyancy, so it will have greater drag than a 'plain' outrigger and a centerboard. Additionally, they will be much more difficult to turn than the alternative. The Hobie 16 example, turns very poorly compared to other sailboats. However, in the case of the Hobie 16, both of those trade-offs are worth it because the lack of centerboards means you can ride right up onto the beach without risking damage to your boat if you don't pull up the boards in time.
In this image of a racing Hobie 16, you can see the crew trapezed out to control the heel of the boat, and you can see the shape of the hull, it's nearly flat facing the water, to resist the sideways force of the wind. The other hull in the water is a mirror image of the starboard hull.
Ultimately, every element of boat design is a trade-off of some sort. As you make adjustments for better and better sailing performance, your result will start looking less and less like a canoe and more like a traditional sailing boat. Only you can decide where there right balance is.