A properly fitted cage transfers all the loads from tube to tube, and should do so without any welding. The welds are in place merely to keep everything in alignment, and rigid, not to sustain compressive loading in place of tubing. Tubing is a strictly regulated thickness and strength, while weld filling an airspace between 2 pieces of tubing has varying thicknesses, hardnesses and strength. On top of that welds in this type of configuration will be very prone to having stress risors, and will not endure fatigue nearly as well.
All of these possible problems come to a head right when you don't want them to. In the case of a rollover where you are relying on your cage to keep you alive, a poorly fitted/welded cage can become more dangerous than no cage at all. As the cage fails you introduce further hazards inside the cockpit, such as broken sections of tubing, or free floating tubing ends, which will make short work of the human body.