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Because the Jin didn't? The Mongols had access to the resources and manpower of the Jin, Khwarazmian empire, the Caliphate of Baghdad, most of the Russian principalities, Kipchaks, Volga-Kama Bulgars, Seljuq atabegs, etc. when they were confronting the isolated Song; primary example being the Mongols' employment of Muslim counterweight trebuchets at the siege of Xiangyang and also the Song surrendering their naval fleet to the Mongols didn't help the Song either. Most of the enemies the Mongols confronted weren't exactly in their greatest condition so it can probably be said that the Mongols rise to power was more opportunistic than many others.
These other territories were really unimportant and played no role in the conquest of the South, literally. Mongke which controlled these areas, failed his invasion, while Kublai, losing these areas suceeded in turn.
In fact Northern China was the only vastly populous agricultural zone under the Mongol dominion, with about 30 million people after the destructions. The Khwarezmian empire and the Caliphates of Iran and Iraq were never resourceful areas. The catastrophic Mongol invasions had annihilated the settled population of Persia with a total population, reducing both Iraq and Iran to populations of around 2,500,000 each. While the population of he nomads of the Inner Asian Steppe, including Mongolia, Transoxiana, Semirecheiye, Jungaria, and the Tarim Basin was certainly no more than 5 million.
The population of Mongol Russia after the Mongol invasion may actually have been as low as 3,000,000, counting 2,150,000 people between Nizhni-Novgorod in the east to Galicia in the west, and 850,000 nomads in the steppe zone farther south. (J. M. Smith, Jr., in "Mongol Manpower and Persian Population", Journal of the Economic and Social History of the Orient, 18 (1975), 271-299.)
It would therefore seem that the whole of the Mongol territory outside of China is only around 14 million people of which only Mesopotamia contain any rich agricultural areas. The rest of the population, been either nomads or sparsely agricultured zone such as Persia and Russia after the devastation of Mongol raids were hardly any economic powerhouses to provide the Mongols manpower or material resources. Not to mention even during Mengge's time, the Khanates are hardly centralized. The Mongol empire similar to the other steppe empires once it gets too large is politically loose like a fuedal kingdom and becomes ineffective in drawing troops from one Khanate to another, rebellions are frequent and the empires are usually short lasted, as in the case of Tujue which broke in two just a few decade after its formation. Similar thing happened to Mongols.