They tried. Not counting Yunnan, 5 major invasions (2 of Burma, 3 of Vietnam/Champa), of which 1 was militarily successful. Judging by the military results, the states in continental SE Asia were not easy targets.

On the other hand, the Mongol invasions were politically successful, in that most of the SE Asian states submitted to the Mongols, i.e., they became Mongol vassals.

After that, why would they try to conquer the area? First, the earlier invasions had shown the Mongols that an attempt to conquer the region would be too expensive and might not even succeed. Second, their main political goals had already been achieved - why would they invade their vassals? Third, while they might have tried to extend their control over the area to direct rule in the long term, there was no long term for the Mongols in the area, since only a few decades later (c. 1320) the Yuan Dynasty was starting to lose control of China with economic difficulties, civil war, and revolt against Mongol rule.

This question has been asked before. A good summary was given by u/krishaperkins in https://www.reddit.com/r/AskHistorians/comments/32ueai/why_were_the_mongols_unable_to_penetrate_into/

Like so many other things in life, it was as simple as being the path of least resistance.

Where the defended Great Wall of China served as a formidable barrier to invading Mongol armies, it could not equal the barrier that the Himalayas and Tibetan Plateau provided for Southeast Asia. Instead, the Eurasian Steppes provided a relatively barrier-less approach to Europe, covered with grasslands favorable for their nomadic lifestyle. These lands were predominately populated by sedentary agrarian communities, considered soft, not much different than the animals herded by the Mongols. In other words, relatively easy pickings. Larger population centers, not so much, but still easier than crossing the Tibetan Plateau and Himalayas (see Fletcher and Neumann).

Even after Kublai Khan gained control of China, marking the beginning of the Yuan Dynasty (1271-1368), Mongol designs on expansion into Southeast Asia were unsuccessful. The Mongols attempted to invade Vietnam first in 1257-58, followed by a second attempt in 1284-85, and a final attempt in 1287. As you mentioned, the environment was not a great one for the Mongols, but logistics and disease also played a part. Perhaps even more influential was the Vietnamese tactics of harassment, including evacuating the capital city of Thang Long (now Hanoi) completely, leaving nothing for the Mongols to raid. Additionally, invasion required naval knowledge, something that the Mongols lacked; the Vietnamese were able to lure the Mongol fleet into the intertidal waters where they were attacked, completely destroying the fleet of 400 ships and forcing the surviving Mongols to flee overland back to China (see “Vietnam: A Country Study”).

So there were attempts, but, as you noted, the environment was not right. In the steppes, the Mongolian armies could logistically maintain themselves locally among the conquered people. Southeast Asia required complex logistic support over great distances overseas, a foreign environment for the traditional herdsmen of the steppe.

For a great read on how much the geography influenced these events (and many others), I suggest Robert D. Kaplan's The Revenge of Geography.

EDIT: Fixed formatting.

References:

Fletcher, Joseph. “The Mongols: Ecological and Social Perspectives.” Harvard Journal of Asiatic Studies 46(1), pp. 11-50. doi:10.2307/2719074.

Neumann, Iver B. “Europeans and the Steppe: Russian Lands under the Mongol Rule.” In International Orders in the Early Modern World: Before the Rise of the West, edited by Yongjin Zhang, Shogo Suzuki, and Joel Quirk. Routledge, 2014. http://eprints.lse.ac.uk/65998/.

“Vietnam : A Country Study.” Online text. Library of Congress, Washington, D.C. 20540 USA. https://www.loc.gov/item/88600482/.