Was the state of Mongolia allowed to exist to serve as a buffer state between PRC and the USSR?

Mongolia successfully seceded from China because of mainly a pastoral/agrarian divide. While during the early Qing Mongolia was entirely pastoral (indeed, guaranteed to be pastoral, though the banner system is another question entirely), by the end of the Qing for a variety of reasons southern Mongolia was starting to see agricultural settlement. Many of these actually turned out to unsustainable in the long run, turning much of the area into desert. Regardless, this meant that the area called Mongolia had two distinct parts - a more agrarian, Han centered part, and a northern part that was more traditional. Many southern princes cooperated and sold land to settlers, despite it obviously working against their way of life.

This caused a deep political divide in Mongolia by the end of the Qing and early Republic, especially as a sense of Han identity developed that was specifically exclusive of Manchu and Mongol peoples. The Mongols, seeing their allies the Qing put out of power, had little reason to stick around other than if they had put down roots - ie, had become agricultural like the south of Mongolia. The Soviets, sensing an opportunity in the early 1920s, supported a bid for independence, but only in the nomadic. The new Republic, not too keen on entering a large war and only really caring about the settled areas anyway, let them go. This divide is still present today - outer Mongolia (ie, Mongolia) is a large and still partly nomadic country that is sparsely populated, while inner Mongolia (a province of China) is agricultural (though more recently extractive) and much more densely populated.

It's complicated why this didn't happen in Xinjiang and Tibet. Xinjiang had a brutal history of rebellions against the Qing, and much of the Qing's budget went towards ruling the area. A large part of this was to bring in a settler population (such that could survive) in order to give a base to public order. The Uighurs and other Turkic groups were largely left to their own devices - they only rarely pushed towards independence in the early Republic simply because being part of China didn't involve doing very much.

Tibet is a story I'm not familiar enough with to comment on thoroughly, though I think some of the independence of the Republic and Qing period explains it. Being part of China was only a problem once the central government started making you do things - at which point the government was often too powerful to resist successfully.

There was a question with the same basic theme a while back : https://np.reddit.com/r/AskHistorians/comments/3yv9uq/why_did_mongolia_achieve_independence_so_easily/cyh3ws5