So the weld is stronger than the welded material.
You are correct but I am not talking about the properties of the base material and filler rod. What I mean to say is concerning welded assemblies and stress concentration. If you can overstress a weldment to find its weakest point and then repair it without gussetting you will still have same problem at the same stress levels. "Weakest link in the chain" situation.
A crack repair is basicly a butt weld and there a few instances where you would see a "perfect " weld ,IE, same filler rod and base material,ground down smooth so that the weld area is the same as the base material ,but not one we would see in most every day life. So usually you would have a lump of excess weld < thicker walled material> of a different alloy <usually stronger> . so your stress point is in the same spot but since the weld is better than the base metal,our crack forms right next to it.
Which is why I suggest gusseting, to try and move the stress concentration point to either an area that has less leverage or to stronger section. I also believe that when I make a gusset I try to avoid using sharp ,square corners. I try to make my plates rounded or ovaled to try minimize me forming a concentration point with my gusset.