Tibet was a buffer state between India and China. The British understood it and maintained that status quo during their era. That is the reason there was peace between India and China during the Raj. India inherited that framework and failed to keep the status quo when China invaded and occupied Tibet thereby bringing their borders adjacent to India's. Protecting Dalai Lama and his subjects, giving them training and keeping them ready for a reverse takeover was India's attempt to push back against China's attempt to change the status quo. It was the right thing to do. The Tibet card is a strategic card with great potential dividends. One does not surrender strategic cards for fear or uncomfortable discussions. And one cannot hold on to strategic cards and expect that there wont be shrill noises from the other side. We took that decision after calculating our national goals and risks.
Having a stalemate with a larger power is better than having peace because it puts you on parity with them strategically, even though you cannot match them economically. Having peace with a large power usually means that the terms of such a peace are dictated by the larger power. That is why India can never have total peace with China, and Pakistan can never have any peace with India. The friction is not because the larger power has imposed it on the smaller power. It is the other way round. The larger power wants a pacified neighborhood because the status quo is already in its favor. The smaller power is forced to cultivate strategic cards to engineer disharmony at the border of the larger power to safeguard its core interests elsewhere, so it tries to alter the status quo. Pakistan has cultivated Kashmir, India has cultivated Tibet. Afghanistan has cultivated Pakhtoonistan. All for the same reason.
China would want to be left alone, and allowed to have Taiwan, Tibet, Xinxiang for itself, but what do we get from letting them have it? We only get concessions from China when we strategically discomfort them. In return, they try to discomfort us but the balancesheet is in our favor. By holding on to the Tibet card, India is able to present itself as a bulwark against Chinese aggression and get concessions from the Western block.
Actually, India was not a smaller power in 1950. Indian population was big. The only advantage china had was larger land but most of it like Tibet and Xinjiang are deserts. Tibet is an extremely resource poor region with nothing useful and mostly a parasitic relation on China for resource. The Tibet is not capable of being independent due to its landlocked nature and resource deficiency. Indian real boundary lies in Himalayas which is the real buffer. Tibet can never be accessed by Indian troops as the himalayas prevent movement of logistics. The chinese mainland is also far away from India, mostly east of the great wall and hence there can be very little direct problems or leverage between the two countries. India and China are only technically neighbours, but the geography makes them quite far apart.
This so called strategic thinking of simply irritating the bigger opponent without basis is nothing short of foolishness. China and India don't have historical enmity. Nehru was an agent of British and hence under behest of USA and UK, Tibet issue was kept alive. Ideally, the goal should have been to take down USA and UK and stop their crony behaviour by allying with China. In 1950s, India was ahead of China in various technological parameters due to USA and UK setting up many industries for WW2. India also had a large enough population and access to the most strategic position of Indian Ocean along with the oil resource of the Arabs. The relation would have been the relation between equals rather than a one-sided relation.
Most importantly, Indian startegic advantage was ruined because India deliberately scuttled defence development under instructions from Nehru. In 1950, the difference between India and China in terms of technology was very much in favour of India. The technology of other powers like USA was also very close to Indian technology. If it was strategic advantage India needed, India would have been quick in developing weapons. China was in shambles in 1950, after independence, had to fight Korean war against a bigger adversary USA, face famines in 1962, 1970 and yet by 1975, China has Satellite launch vehicle, ICBM, nuclear submarine and thermonuclear bomb. Indian strategic advantage turned to disadvantage due to willful neglect of military technology by Nehru, not due to size of China being bigger.
The real reason of enmity between Pakistan and India is out of Islam. Kashmir was considered as muslim majority area that rightfully belonged to Pakistan. This is also the reason why there is no hostility between Myanmar or Nepal despite boundary disagreements. In Afghanistan, Pakistan was a close ally till about 2000. It was the USA's invasion and installment of puppet govt in Afghanistan is what causing problems to Pakistan.
It is unnecessary to have unnecessary enmity just out of size difference.Do you see enmity between canada and USA? Do you see enmity between UK and France? There is one thing which is about differing in decisions and another thing in fanning separatism and calling it leverage. Hosting a separatist regime and calling it "govt in exile" is too serious form of foolishness without objective.