Is the only reason for the quarter circle in the corner to create an edge to distribute the force to avoid a high stress that was seen when the load was applied to the vertex?

The problem you introduced by making the edge was the force moved away from the vertex.  You can overcome that problem by using a Remote Force. In that way, you can have a separate definition of an edge to distribute the load and the location in space of the point of application.

If you use a Remote Force, you don't even need the quarter circle. You could just select the vertical edge of the 2D part and position the point at the vertex.