From what I know about welding, in this case TIG is definitely a waste of time or the wrong application. The difference in filler added will be minimal, and even with a factory new chassis there might be too much contamination to get TIG to work properly. TIG is best used in specialty...
Stiffer is always better so that the suspension can do it's job more effectively and so that you can put power to the ground. Even on modern WRC cars they still stitch weld when they prep the chassis.
Downsides is increased NVH and increased cost of repair. When the seams are all welded...
