The Mongolian settlement concerned racial as well as strategic issues. Soviet Union naturally wanted it to remain as a buffer zone between Russia and China, just like the good old days since Song Dynasty.
Mongolians, like Koreans, had never been racially part of China. They still wanted their own country even if there's no empire anymore. China, of course, would want the whole of Mongolia "back" just like the case of Manchukuo (Manchuria). China didn't got it all back but in fact, China got the better part of the deal.
The redrawing of boundary divided historic Mongolia roughly into equal two parts. The southern half known as Inner Mongolia Province of China now, has the better built-up, settled, fertile and productive lands with more than 20m population. The northern half, the independent Mongolia now, are all the plains with less than 3m population.
The US/UK war aim was to prevent Japanese dominance over the Far East and East Asia. That meant first and foremost, to help China repel Japan. That naturally entailed also forestalling the possible emergence of China as another Japan. Blame US/UK? I think not. They have to protect their own interests first, just like anyone. Blame China itself. If it was strong enough not to need foreign help, it could do whatever in its best interests too.
