Hang on, in 1971, Bangladesh was East Pakistan at the time, which was why the Pakistan army was there. That was when Bangladesh was fighting for independence, and the people spent six months fighting the Pakistan Army to try and get independence. The Pakistan Army was busy trying to prevent this, and engaged in some brutal repressive techniques.
It was a civil war/war of independence (delete according to taste), and it involved some of the most egregious acts of terror it has ever been my misfortune to witness. Into this, once the monsoons had cleared, the Indian army came, ostensibly to restore order (which they did with a level of competence and professionalism that was praiseworthy). They may well have had other motivations, although as a lowly Royal Marine stuck protecting the British Embassy while the Hell was going on around him, I didn't pay much attention to deeper political questions.
The Bangladesh people welcomed the arrival of the Indian army, because the Indian army put an end to the terror that the Pakistan army was inflicting upon the Bangladesh people.
I make no claim to being a dispassionate, objective observer of that particular passage of history, but your statement is not in accord with what I witnessed.
I see no contradiction- the Indians chose the correct strategy. Concentrate on East Pakistan/Bangladesh and destroy the Pakistani army there. they do it with ease as the people welcome them as liberators. Getting the Bengalis to accept a quasi independent status with India in control over the defense and foreign policy would be easy. I was well aware of the reasons for the war. The result of the Bengali campaign though, is that over half the Pakistani army was captured
But the Indians didn't stop there. They also launch attacks into West Pakistan. There the government had more support but not all that much. From a military point of view, the Pakistani army was beaten and could offer little real resistance Most important, the Pakistani army knows it was beaten and its resistance was crumbling. In fact, most of what was left of the Pakistani Air Force was hiding in Iran There's little reason to expect a long drawn out conclusion
Since the proposed peace terms are exceptionally mild- control over defense and foreign policy with local self government- there isn't likely to be much reason to resist either
Also to answer your question:
1. The UN, which was created so that a country fully annexing another nation couldn't happen without just cause. Why would India just decide to annex Pakistan?
2. See #1
3. The UN had the ability to intervene. If India says "fuck you" and annexes Pakistan and Bangladesh there would be harsh sanctions, maybe even an embargo if India does go Hindu Nationalist.
The Same UN that sat quietly by while the Vietnam War rage, the Vietnamese annexed Cambodia ad infinitum Add in that the Soviets could and would veto any act against India, we can dismiss this body.