The problem with having a single autocrat in power is that the potency of your entire empire is contingent upon the potency of the autocrat.
Genghis Khan was clearly the cream of the crop when it comes to quality human beings. He was shrewd, intelligent, fierce, strong, ruthless, quick in mind and agile in body, far seeing, a master strategist and logician, a powerful warrior, wise, and generally probably one of the most capable human beings ever to have lived. He was also, quite surprisingly, a very humble person who was not motivated by power. In spite of this, the power he wielded was tremendous beyond compare.
Were he alive today, he could be many things. A CEO, a politician, an mma fighter, a team athlete, a lawyer. Seriously, anything, I believe, Genghis would have crushed in most contexts.
Let me ask, how do you simply replace such a leader?
The Roman Senate was able to survive because even without a powerhouse like caesar ruling as a tyrant, there was enough of an infrastructure in place to accommodate losing a strong leader. They didn't have to replace caesar.
With the mongol empire, Genghis was it. He was the head, neck, and body. When he died, it wasn't possible to just replace him. The descendents of the Khan to come later simply weren't cut from the same cloth.
This isn't surprising given that Genghis observed that if he didn't regularly send his men back to the steppes, they grew "soft" and weak. Genghis grew up under absolutely horrible conditions. He was often poor, often without a leader in his family, captured by the age of 10, and had to kill his older brother by 13. At 14, his wife was taken until he was 15, when he rescued her. She was pregnant, likely with her abductor's child. Genghis raised this child as his first son. Seriously, just to underline what a unique and special kind of person he was. Atrocities or otherwise, temudjin was a BOSS.
Think about how absolutely brutal that life must have been, and how such a meager life made Genghis resourceful, intelligent, and strong, and very very hard to kill, an enemy to be feared by all. Now, imagine his grandchildren growing up in some Chinese palace, surrounded by decadence like furniture and and warm water baths.
These weren't the same kind of human being.