USA, Europe and other Western countries have a direct interest in preventing the territorial growth of China. West has a stake and a physical interest in preventing the expansion of China's borders. And it has nothing to do with rivalry or ideological war nor does it have anything to do with Western people's love for Tibet etc. These notions are superficial bullshit. The real reason why all Western leaders would take personal interest and would literally lose sleep thinking about India-China tensions is explained below.
China's actual population is multiple times the officially stated figure and it is growing exponentially. China's real population is already at least 6 times that of the next most populous country. And this staggeringly high population is spilling not only outside it's borders but all over the world. Wherever you see, you will see Chinese. Be it in China's neighborhood like Singapore (my friend had been to ground zero of Singapore), be it my own little sleepy town in interiors of India, be it Pakistan, be it facebook pictures in USA, be it Africa, be it Eastern Russia where Chinese marry Russian women and so on. No wonder China has border disputes with most, if not all, of it's neighbors.
If China is allowed to expand, someday Chinese may end up on Western shores seeking refuge in developed countries due to mismatch in Chinese population and Chinese material resources. Due to shortage of resources, the Chinese race may try to occupy Western countries if their population is unchecked. The population of sparsely populated Arab countries is giving West a nightmare (Reference Arab refugee crises). Imagine what the super dense population of China can do. The technologically advanced countries of USA and Europe would intervene in India-China conflict to keep the Chinese populace confined inside China's borders.
This fear of West is forbidding China from attacking India. In behind-the-scene diplomacy, Indians have been blackmailing China about this dirty secret of China's real population number. Indians have been telling to Chinese, "Back off or else we will tell Uncle Sam that your large population can be a threat to West merely due to it's flabbergastingly high numbers and then the technologically superior West will nuke you."
USA would 'protect' India not because of fantastic and abstract concepts like cold war or for real but implausible factors of moral grounds but because of earthly selfish reason of protecting their physical bodies from the teeming Chinese hordes bursting at the seams.