The Kashmir issue has three proponents, India, Pakistan, and the people of Kashmir. Indian claim to Kashmir is based largely on the instrument of accession signed by Maharaja Hari Singh which is entirely legally valid. The Pakistani claim is based on the Muslim majority in the area which is logical. And the people of Kashmir want a separate state due to decades of neglect. Estimations indicate 65-70% people opting for independence in case a plebiscite or referendum is ever held.
But in reality any such referendum is a pipe dream by Kashmir's inhabitants. Kashmir has tremendous strategic value for the defence of both countries. Plus any loss of territory, even ceding an inch would result in immense loss of face and would be tantamount to political suicide for both the regimes. Added to that is zero support from the international community as a separate Kashmir represents a grave threat to south Asian stability.
India seems content with the current status quo, and has made no overture towards the part held by Pakistan. The reason for this is that Indian held area is much more valuable in wealth of resources than the parts under Pakistani or Chinese control. Added to that the completely Muslim population of the Pakistani part as well as the difficulty in access from the Indian side, results in total lack of interest by India in Pakistan's part of Kashmir. Hence for India Kashmir seems to be a settled issue.
On the other hand, since Pakistan got a raw deal in the division of Kashmir, it has engaged in unsuccessful wars and extremism to gain ground in the Indian part. And keeps on raking up the plebiscite issue. Knowing fully well that were a referendum ever held, Kashmir's inhabitants would in a majority choose independence from both countries. And like India, Pakistan would be extremely loathe to lose an inch of it's currently held territory. Hence the plebiscite call by Pakistan is a hollow one, mostly political grandstanding, while simultaneously executing actions like changing the demographics which ensure a plebiscite can never be held.
No one wants a separate and independent Kashmir, not India nor Pakistan, nor the international community, apart from the very people of Kashmir. At best the people in Indian part of Kashmir can hope to eventually improve their living standards due to vast amount of aid by the government of India to the state, much greater than is provided by their Pakistani counterparts.
All three current occupants of Kashmir, India, Pakistan, China are nuclear powers with more than a hundred warheads each. Which ensures none will use it against the other. None of them wants to see any change in status quo.
Now, even though I feel sorry for the populace of Kashmir, any dream of independence would remain just that, only a dream in the foreseeable future, owing to the harsh ground reality and real world scenarios opposing that. When no plebiscite has occurred for 67 years, rest assured it'll not happen this century..