Pakistan in 1971 was still far smaller than India, it was your historical complex (deeply embeded from the events of the previous millennia), a mere figment of your imagination, that was a two-front war. East Pakistan never had the military prowess to ensure that possibility, its air force and armoured columns were quite insufficient when compared to the West Pakistan. In 1948 and throughout the border skirmishes uptill the war of 1965, this Indian establishment's theory only proved to be nothing but a paranoia - even during the 1963 Indo-China war, India was worried if Pakistan would open its front, but we did not despite doing militarily and economically far better than India.
Which events of previous millennia? There were just two reason.
First was a huge problem of refugees post brutal massacre done by East Pakistani army in East Pakistan. Dont believe me? Look at the current Rohingya crisis that BD is facing. Indian Leadership was wise enough to intervene and avert this crisis to fall into sensitive areas of WB.
Second, strategically speaking, your current abilities are never the lone factors in deciding such matters. That time Pakistan was not having enough military presence in East Pakistan. What stops Pakistan from creating a build up in future? Or allowing some foreign power to encircle India, that time it was USA.
BTW, Pakistan attacked India in '65 after seeing lack of prepration during Indo China war.
What happened in 1971 has a far-reaching impact, you have antagonized your eastern front till eternity. Your helped forged an alliance that probably wouldn't have existed in its current state had there been no 1971. Pakistan then helped the red dragon to reach out and open up to the Western world and contributed with its part to help them become a major world power four-decades later. This alliance has encircled you from your entire east to entire north and north-east and in the process choking all the natural and historical trade routes of mother India, something that has not happened in history - with China loooming large in the North-East, your Chicken neck is far more vulnerable than ever before, seven-sister states issue in this scenario can only become a trivial issue.
Actually, instead of antagonizing, we have created a much easily dealt situation in our eastern side. BD for all her issues with India, is no where as mortal enemy of India as Pakistan is. Infact India enjoys quite a comfortable relationship with BD in terms of co-operation on geo political and security issues. Heck we were able to solve one of the most complex border situations of enclaves and exclaves with BD very recently. Do you see India BD border having as much military deployment as you see in Indo-Pakistan border? I doubt it. We only antagonized West Paksitan. But then we are mortal enemies anyways.
As far as China goes, in 71 China was no where in the picture on the worlds map. And even before China came in the picture, you were courting America which was pretty anti India back then owing to India's cordial relationship with USSR. Putting it bluntly, you have always done your worst against India so cutting Pakistan into half was an apt decision. Lastly, China-India feud is not Pakistan centric. We have our own issues to tackle. With Pakistan or without Pakistan, we will have to deal with dragon. So you are overestimating your contributions in this. Any party which would have shown you a wad of cash would have bought your help.
On the north east, actually you have not noticed. India is creating an alternative route to North East via BD. It would have been impossible if it was still East Pakistan.
I am not suggesting that an Indo-Pak war would involve China (unless you try to attack Gilgit-Baltistan) so practically a 2-front war is out of the question but lo and behold, since the historical complexes still exist in the Indian mindset your Chief of Army Staff Bipin Rawat came up with idea of 2.5 front war - so 1971 took nothing away from Indian psyche and while further deteriorating the geo-strategic situation for India.
Put it simply, I like the 'Hope for best and Prepare for the worst' attitude of Mr Rawat.