What are the benefits of a 'cranked arrow' delta wing?
The main benefits are:


High root thickness, so the wing can be made stiffer and stronger where the loads are highest.
Better pitch stability in the post-stall region, so no AoA limit needs to be observed. The X-31 could maneuver with thrust vectoring only because its cranked arrow delta wing was more or less neutral in pitch over the full AoA range. A simple delta wing produces strong pitch-up moments in the post-stall region wich would quickly overpower the moments possible with thrust vectoring.