And if you know anything about Indian foreign policy, India vehemently opposes any third party mediation, especially US mediation.......(all said and done there are still some trust issues). India goes to Washington only to tell US to muzzle up her dog that's all.
American options currently with Pakistan are already very limited and if Pakistan goes out of control then you actually have none despite all your political and military resources. You would have to simply work out a strategy with India. Bush government recognized this problem early on and hence decide to get closer with India.
As for the Bin Laden raid, I highly doubt US pulled it off with just Chinooks and Apaches. Somewhere somehow Pakistan Army was part of this. Even though most of Pakistan's air defense is concentrated on the eastern side it would still not have been a cake walk for Apaches to fly in unopposed. And lucky for the US, it is geographically isolated from any threat of retaliation from Pakistan. Its not something India can enjoy even with substantial military capability.
Secondly India has over 600 military helicopters (including Mi-17V,Mi26, Mi35 and Hal Dhruvs). NONE of US allies have that many. The RAF may have a few Chinooks but still nothing on India. A few Chinooks and Apaches that India may buy will help replace India's aging fleet but wont add anything substantial to change the paradigm of Indian military doctrine/tactics against Pakistan.
As for a broader counter insurgency role, I think India has actually gained more experience and fared better then US. In Kashmir where India for decades faced the same enemy Russians faced in the past and Americans are facing at present, terrorist insurgency has been reduced to near zero. There isn't an inch of Indian territory that India has lost control to Mujaheddin. Cannot say the same about US in Afghanistan despite all the military assets at your disposal.
If Pakistan comes unglued, India is more likely to be the immediate target of loose nukes than the US, which you later describe correctly as "geographically isolated from any threat of retaliation from Pakistan." And, as Bin Laden's Islamist critics contend, attacking the US on 9/11 was foolish because it provoked a devastating response against Al Queda and its allies.
Many of the details of the Bin Laden raid remain hidden, but I too am sure that more than a few Apaches and Chinooks were involved. That supports my point, that carrying out such a raid called for a wide and deep military capability that the US alone possesses -- and on a global basis, at that.
My understanding is that India is eying getting a relative handful of Chinook and Apache helicopters for its special forces. Of course, as you contend, it will take more than first rate helicopters to carry out a Bin Laden type raid deep into enemy territory.
As for implication that the US is "losing control" of Afghanistan, we never desired to have control of it. For better or for worse, the US is now disengaging, hoping that it can provide enough support to maintain a relatively friendly government in power in Kabul.
If not, Afghanistan's neighbors -- Pakistan, India, Russia, and China -- will have to pay the heaviest cost for the ensuing chaos. If so, will India be ready militarily?