The problem comes about when the weld and adjoining base metal cools. As the weld is being deposited, the base metal is heating and expanding. Once the weld is completed, the weld and the adjoining base metal cools. In doing so, the weld is contracting, thus pulling the pipe further into the joint. As the pipe is pulled into the socket, the gap is closed somewhat. Were it not for the presence of the gap between the end of the pipe and the shoulder of the socket, the weld root would be placed into tension resulting in a root crack unless the weld is very ductile (as is the case with austenitic stainless steel).
Welds that are high strength with low ductility tend to crack when the welder forget to leave a gap between the end of the pipe that is inserted into the socket fitting and the shoulder of the fitting. As mentioned, the codes require a minimum of a 1/16 inch at the time the pipe and socket are fitted together. When these same joints are radiographed, it is common to see the gap is less than 1/16 inch. Again, the reduction of the 1/16 inch dimension is the result of the weld contracting upon cooling and drawing the pipe further into the socket. The larger the fillet weld, i.e., the more weld passes deposited, the smaller the gap becomes.
The suggestion that the weld against the pipe be made larger is something practiced by the U.S. Navy for many years. The nominal fillet size for Navy work is T by 1.75T where T is the wall thickness of the pipe. The long fillet leg is placed against the pipe. It has been shown to increase the life expectancy when fatigue is a consideration.
A good friend did his Master's Thesis in this very subject.
Best regards - Al