Genghis Khan was said to have originally planned to depopulate north china and replace it with pasture. However his advisors wisely told him that living chinese pay more tax than dead chinese. What would happen if he stubbornly attempted this anyway?
Nitpicking: AFAIK, the anecdote was related to the reign of Ogdai, not to his father, and the idea was associated not with the Khan but with few noyons sticking to the traditional views.
Genghis, after the initial success, delegated the North China theater to his general Muqali with the
hereditary Viceroyal title and left to fight elsewhere. Muqali is well-known for his conciliatory policy which allowed him to increase size of his army dramatically (by at least 7 tumens; initial size of his army was between 20 and 30K) and to keep the subdued parts of the Northern China under control (mostly by retaining the existing administration). The alleged episode is attributed to the time after conquest of the Northern China was completed and most probably is a legend serving to promote image of Yélǜ Chǔcái as a wise statesman: by the time when discussion presumably happened the Mongols were well aware of the basic facts of life including one that you need skilled people to produce silk, iron, silver, wine and grain (the items which the Mongols needed and could not produce themselves).
Back to the subject. Well, if the idiotic view prevails then the Northern China has to be conquered again because Chinese troops on the Mongolian service would probably object to their own extermination. After this is done, there could be problems with getting the needed goodies (see above). And, of course, there could be technical problems with the implementation just based upon inequality of the numbers and absence of the machine guns, strategic aviation and other things helping to kill people in really big numbers.
Of course, if one assumes a purely "environmentalist point of view", it could be argued that the proposed program would be conductive to the lesser production of CO2, consumption of the natural resources and other benefits (especially in a long run). It can also be argued that (if extended to the Southern China) it would eventually prevent unpleasant things like theft of intellectual property, unfair trade practices, etc. [just kidding

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