Indian mobilization was aimed as much as at US and as at pakistan. Even then some of the results of coercive diplomacy are not so quite evident.
I fail to understand how, coercive diplomacy works if one side has overwhelming military muscle over the other side. Clearly that is not the case in the subcontinent, that is why even after trying to flex military and diplomatic muscle several times, India has failed to change GOP's position.
1. Musharraf suddenly 'understood' Indian position.
Musharraf is a military man first and a politician second. Op Parakram emboldened PA's General Staff and Musharraf became convinced after this operation that PA was in a much better state to fight India. Mobilization of divisions from as far away as Balochistan and KP speaks volumes of the preparedness of PA and Musharraf personally took credit for that as he worked very hard to correct the deficiencies in PA, especially when it came to mobilization.
2. US tilt towards India, and at least the congress
That was something that was bound to happen. Pakistan and US interests were never the same and the US needed to promote a power that will form a counter weight to China.
3. Nobody seems to utter K word now a days, not to hurt indian 'feelings', as if pakistanis have no 'feelings'
Nobody ever did as the world was much more busier with their own interests and Kashmir has no oil so the world couldnt care less what happens there. Also the reason why insurgency in Kashmir died down as relations between both Pakistan and India improved after 2004, Pakistan used its leverage and put a tight seal on the insurgency. Also, many of the veteran Jihadis left for Afghanistan as to them the US was a bigger enemy as compared to India.
4. The world in general(US, the primary defence supplier of pakistan in particular) is more open to unilateral war/strike from India than ever before.
I have no idea where did you come up with this analogy. The world and primarily the US are sh** scared of a strike from India, the amount of diplomatic effort that was put by the world and especially the US is a testimony to that. Dont for a second think that the world will take sides in a military duel between India and Pakistan, the world and especially the US will demand an end to all military hostility as the stakes are too high.
I would argue not going to war was the right thing to do. What would it have achieved that we did not achieve. Was stopping the terror in Kashmir a coincidence? Or was it bargained? Would we have achieved that with a war?
The Indian public wanted vengeance, they wanted blood for blood and this is exactly what the IA was ordered to do. The biggest mistake the Indian public and the politicians made was that they overestimated there power and underestimated the power of there enemy. At the time there was no objective, the only objective was to launch a punitive strike on PA to humiliate it and degrade it in front of the Indian public.
Dont make the mistake to think that Op Parakram had anything to do with the insurgency weakening in Kashmir. The primary cause for insurgency weakening in Kashmir was due to the fact that many veteran Jihadi fighters whom were the leaders left to Afghanistan to fight on the US as they believed that the US was the bigger threat. As relations improved between both India and Pakistan, Musharraf used his leverage and completely put a lid on the insurgency.