Genghis Khan was certainly ambitious and had much larger desires in the world than merely uniting the warring tribes of the steppe. Yet, in order to expand his empire, he needed someone to rule the newly conquered people. he had to leave someone in charge. ideally, he would have had a stable of talented sons and given each one of them a newly conquered country to govern, but his sons were simply not capable. Without competent sons, he could leave a general in charge, but Genghis Khan had been betrayed too many times by men inside and outside his family. He probably knew well the result of Alexander the Great's overreliance on his generals, who subsequently divided the empire among themselves as soon as their leader died ...
Genghis Khan's mother and wives were too old to take command of these new nations and to enjoy the full benefits of what he had to offer, but he had a new generation of women who seemed as capable as the previous ones.
Women ran the largest empire on earth and that too in the 12th-13th century!
Not bad. Not bad at all.
Actually an Indian would not be surprised. Razia Sultan ascended the Delhi throne around that time. She was the first ever woman to rule in the Muslim world.