You can't weld on a sway bar because the heat makes the metal brittle. This makes the sway bay less flexible and more prone to breaking. A sway bar cannot function properly if it cannot flex.

 

I can understand placing a welder onto a piece of metal for a considerable time would make it less flexible but we are only talking about spot welding a washer on the end of the sway bar. In fact the washer spot-welded on would be on the other side of the bushing and would cause the sway bar to be any less flexible.

This would be two quick shots and would not make the metal brittle...they are surface welds. Hot Rods with I beam chassis' have had similar welding done on their entire length in order to box in the frame. Welding on the washer is much less intrusive.