There is 3 billion people between China and India, and a two dozen dead over frigid uninhabitable frontierland is not going to derail the broader strategic relationship.
I'm not very worried that India will ally with US against China, precisely because Indian memory of Anglo-Saxons pitting Indian princely states against each other in a divide-and-conquer fashion to eventually create British Raj over Indian subcontinent. Indians won't be so easily used as frontline guinea pigs against China, and the current disputed frontier is a legacy of British imperialism in Asia. There is no inherent animosity between India and China except left due to British colonial legacy.
If you want to be a pawn of someone,you must prove you have the capability to be a pawn. The question is the Indians are really useful to the US? Weak,hungry,social dividing,the US really wants such an ally to fight China? As a Chinese ,I am more than happy to see the US allied India,that will only add a billion good for nothing to it. We call the ally like India"猪队友"。
Looking from India's perspective I can understand its urgency. China effectively controls the entire Tibetan plateau highlands except for IOK. It would be akin to encountering fortress clusters on top of a cliff side but it's situated right next to your heartland while being thousands of km from China's heartland. This creates a permanent siege emplacement in favour of China.
To mitigate the dangers of this situation, India would seek to increase its footholds on the highland, plug choke points and avoid spreading resources too thin along the front(s).
A straight line path from which is located north of Uttarakhand state and south of G219 highway to downtown New Delhi is less than 400km. This would put the capital within the range of many mobile land based weapons in China's arsenal, such as WS-2D, SY-400, DF-15, etc. The geography makes counter battery difficult without achieving air superiority over the north side of the Himalayas. Guided weapons can disguise their launch location and unguided ones can be relocated.
India for a while was reluctant to build transport infrastructure along the frontier to prevent it being a double edge sword to be used against it in case China gained the upper hand in a potential conflict. Some of that has changed during the Doklam standoff. Doklam applies pressure to a sensitive point for India, the Siliguri corridor. A sole 20-25km wide corridor connecting mainland India to the North East, containing one highway and a few local roads. Logistics are under threat. A drive from Doklam to Siliguri is 160km (including winding roads) with an estimated drive time of 6 hours. A straight line path is about 90km from the Doklam plateau, putting the corridor within range of most of China's MLR systems and can be effectively be mined remotely and roadways disabled from guided munitions.
Another vulnerability of the Siliguri corridor is being flanked by Bangladesh and Nepal on both sides. Having friendly relations with these neighbours would be essential for security of the corridor.
Positions on Doklam can literally see Bangladesh (100km) and the Siliguri corridor (90km). It is the last high ground before the Ganges plain. South Asia is within visual distance of the PLA. North East India is at risk of being isolated in case of a major conflict. Isolation could result in independence of the region from India and logistics for commerce facilitated through Bangladesh and China (using infrastructure built by India to prepare for conflict). This will create new buffer state(s) between India and China, enabling concentration on the Western Tibet front, furthering the distance from the Chinese heartland and increasing strategic depth. The long term strategic implication is the possibility of introducing China as a major South Asian/Indo-Pacific power, facilitating close ties between China, Bangladesh, Nepal, Bhutan and North Eastern states.
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I don't have a viable solution for India as of current. Just want to illustrate the situation I think India is facing.
If there was any strategic rationale on China's part, I think the best explanation is that these actions are designed to bring India to the negotiating table again in restarting the process of officially demarcating the border. China wants to have clearly defined borders with all of its neighbors, and concentrate its efforts in expanding its influence globally. Unfortunately, it seems that successive Indian governments have felt that any border treaty with China would not be politically tenable, for unclear rational reasons. Then again, rational decision making may not be the best description of what passes for strategic discourse over the himalayas.
I do see that the thread is starting to drift somewhat off topic.
I will however give my view on the overall situation.
I would say that Pakistan is still India's number 1 concern, not China and that when you see the larger regional map, it is Xinjiang that catches my eye, rather than Tibet.
To that end, I would see India far more interested in being able to expand its influence/occupied territory north towards Xinjiang in order to isolate Pakistan and to disrupt the CPEC. I could see the US also being interested in such a strategy.
The potential danger would be in a situation where a lot of regional unrest is created and so the US inserts itself in a "Peace Keeping" role.
I say potential danger, as every time I try and make a realistic scenario out of the theory, it falls apart really fast.
You can look at previous US insertion operations such as Afghanistan or Syria, but these are small nations and this would not be possible against Chinese territory.
The closest (but far from comparable) situation is that of the Ukraine and here we see no US military placement anywhere near where they risk contact with Russian forces.
In short despite the great power dreams of lesser powers and the desires of greater ones, the situation in Ladakh is one of Tactical positional competition. A competition which China is very much winning.
If India finalized a border treaty with China, then it can redirect its resources entirely to dealing with Pakistan.
It's not because of Pakistan. Praveen Sawhney explained it in one of his recent videos. He put it very simply: When India joined the "quad" and decided to lead the charge in "containing" China, it crossed a red line. Basically, India has raised itself from being a tactical threat to a strategic one.
This is why China is demanding something in these "talks" which it knows India won't agree to. China has no intention of retreating from these hills, because now it can cut off India from supplying its northern sector. This move is countering India's open threat to China's CPEC project, which is also tied to strategic supply lines. China has locked in its position on the ground now, because India has made its hostile intentions clear.
Sawhney also said in one of his older videos (pre-Ladakh) that China has permanently shifted its strategy on India. China has been waiting for India to show good will for decades. Now, that era is over. India entering the US-led "quad" is the main reason. China needs to position its forces in a way that it can threaten to damage India if it decided to damage China.