Yay, someone supports my idea

It is true, AI Mongols have large stacks of keshiks... But most of the time, they linger around China, Mongolia proper and Manchuria. Sometimes they invade Korea. By the time Mongol conquest goes international, it loses a lot of steam and the empire is already at an economic/technological loss. It simply spreads too thin, and too vastly. For instance, AI Russia 4 out of 5 times repels them after a small scuffle. Sometimes the scuffle prolongs for several centuries, as Russia begins to expand into Siberia and encounters Mongol settlers/soldiers.
But AI Mongolia is still stable. So, proper "motivation" would be needed. That is where the barbarian spawns come in. Some barbarian spawns over Samarkand, Merv, the Silk Road on general. Maybe some spawns over Chechnya, Continental China and Korea, should these locations have been occupied. They don't need to be huge armies per se, just a couple troops; so that the barbarians themselves don't over expand. While a Human Mongol player could overcome this problems with ease, for they will have built a functioning empire; the AI just can't. The AI will lose the frontier lands, encouraging eliminated civs to respawn and encouraging expansion by still existing ones. It will most likely keep Mongolia proper and parts of China, for those parts tend to be thick with Mongol troops.
So yeah, unless AI Mongolia is cunning; it will feel the impact. A careless Human player will do so as well, so it's a win win