Dr. Seuss and Stuck.
While your questions seem good in nature there is a very simple answer. The Baal Shem Tov had said before his death that Lubavitch was only going to have 6 leaders, at the end of the last Moshiach would come. Granted it was left wide open which is also why the Rebbe never had any children, as they felt from the decree in Shamayim was correct the could never discuss or point towars a new leader. I am not Lubavitch but I have spent time with them and have many open discussions with them. I dont attack them for there beliefs nor should we, as a Jew in order to bring Moshiach, Rav Frand said it best We must have Achtus as nation for a good din that will ultimatley bring us Moshiach.