“Why was he the first rebbe that did not have a successor?”
This is a question you should address to someone in a leadership position in Chabad.
With respect to leadership, is Chabad any worse off than many other chassidussis (best I can do for the plural of chassidus)that have splintered, despite apparent successors being named? Would you prefer Chabad of 770 Eastern Parkway and Chabad of Utica Avenue?