The de facto border carved in 1949 worked to India’s territorial and political advantage.
The  ceasefire line left the Indians with the bulk of Jammu and Kashmir’s territory (139,000 of 223,000 square kilometres, approximately 63 per cent) and population. The Indians had gained the prize piece of real estate, the Kashmir Valley, and they also controlled most of the Jammu and Ladakh regions. These areas became Indian Jammu and Kashmir (IJK). The Pakistanis were left with a long strip of land running on a north–south axis in western J & K, mostly Jammu districts bordering Pakistani Punjab and the NWFP . . . a slice of Ladakh (Skardu), and the remote mountain zones of Gilgit and Baltistan (the Northern Areas or NA). (Bose 2003: 41)
And claiming the rest is probably undesirable anyway...
Despite the bombastic statements and blustering of the governments of both India and Pakistan, however, the Indian government has all along perceived the inclusion of Pakistani-administered Jammu and Kashmir and the NA into India as unfeasible. Likewise, the government of Pakistan has all along either implicitly or explicitly acknowledged the impracticality of including the predominantly Buddhist Ladakh and predominantly Hindu Jammu as part of Pakistan. The coveted area that continues to generate irreconcilable differences between the two governments is the Valley of Kashmir.
Those are quotes from an article by Nyla Ali Khan
That's in line with the fact that during the Dixon mediation India wanted a partition or a region-by-region plebiscite (likely resulting in the same), while Pakistan insisted on a plebiscite on the whole area, or a partition on religious lines.
According to the Indian commentator Raghavan, it was first Nehru who proposed a partition-cum-plebiscite plan: Jammu and Ladakh would go to India, Azad Kashmir and Northern Areas to Pakistan, and a plebiscite would be held in the Kashmir Valley. Dixon favoured the plan, which bears his name till this day. Dixon agreed that people in Jammu and Ladakh were clearly in favour of India; equally clearly, those in Azad Kashmir and the Northern Areas wanted to be part of Pakistan. This left the Kashmir Valley and 'perhaps some adjacent country' around Muzaffarabad in uncertain political terrain. However, according to Dixon, Pakistan "bluntly rejected" the proposal. It believed that the plebiscite should be held in the entire state or the state should be partitioned along religious lines [Which would have given the Valley to Pakistan].
This was basically the Indo-Pakistani version of a gerrymandering dispute.
After the failure of the UN mediation(s) came the 1972 Simla Accord in which India and Pakistan agreed to solve Jammu and Kashmir problem bilaterally, without involving anyone else.
Both governments agree that their respective heads will meet again at a mutually convenient time in the future and that in the meanwhile the representatives of the two sides will meet to discuss further the modalities and arrangements for the establishment of durable peace and normalization of relations, including the questions of repatriation of prisoners of war and civilian internees, a final settlement of Jammu and Kashmir and the resumption of diplomatic relations.
So not only is India actually pretty happy with how the Jammu and Kashmir is partitioned (despite the continued official rhetoric to the contrary), but they also gave up on involving anyone else in the resolution, and the latter in agreement with Pakistan.