don't hold your breath. They are relevant because they are true leaders of their people. And you don't need a position to lead. And before people here start dissing them, all three in question, Abdulla, his son and Mehbooba are the best things India could have had. While people in the valley were baying for blood, this gang managed the impossible- win their elections and still maintain a balanced relationship with India. No one in the valley had the guts to come in front of cameras and claim that India is secular because Hindus are the most secular people in the world- farooq Abdulla did when BJP was winning all around. He has every right to be heart broken. It is important for us to let him know that our vision is not to take the unique identity of Kashmir but that we have a compelling way forward. India is not a country where you can pound people into accepting authority.
The fallacy in your argument can be described thus - When Sheikh Abdullah insisted on autonomy post Maharaja Hari Singh's signing the Instrument of Accession with the then GoI and appointing Sheikh Abdullah as the Prime Minister of the state of J&K, Dr Ambedkar told him in no uncertain terms that the IA weren't there to sacrifice their lives so that J&K became an independent entity.
Sheikh Abdullah being the typical Kashmiri ( more crafty as compared to thr Pashtuns who're more renowned for brawn than brains) always harboured notions of being a sovereign in an independent J&K.He did this by playing India & against Pakistan by convincing Nehru that he was the best person to be an emissary between Islamabad & Delhi.
Nehru understood his game a bit late (?) But acted on it in 1953 ( See Kashmir Conspiracy Case where in Sheikh Abdullah & his cohorts actively collobarated with the Pakistani establishment to overthrow Indian rule in J&K.Also refer to the Plebiscite Front) , wherein he got Karan Singh the then Sadr e Riyasat to dismiss Sheikh Abdullah and have him jailed. Sheikh Abdullah remained incarcerated for 11 years till Nehru decided to suspend the trial under the Kashmir Conspiracy Case and withdraw all charges, accepting Sheikh Abdullah's initial suggestions of playing emissary between Ayub Khan's government in Pakistan and Pt. Nehru's in India. The details of what exactly were discussed & agreed upon remains a mystery for Nehru passed away during SA's visit to Islamabad and he cut short his visit to return to Delhi to attend Nehru's funeral.
Shortly after that the 1965 war followed with Sheikh Abdullah being incarcerated once more till 1968 and exiled from Kashmir in 1971 with the banning of the Plebiscite Front. After India aided the creation of Bangladesh in 1971 & the Shimla accord , SA came to the conclusion that his dream of being a sovereign in an independent J&K was over and initiated talks with IG culminating in the IG SA accord. Wikipedia is a good primer for the history of all these developments, in case you're interested.
The salient lessons drawn from this is any party assuming power in Srinagar knew they were under Delhi's eye. By signing the accord with IG, SA was viewed as compromised by a section of the population in J&K notably the JeI in J&K ( which is headed by Syed Geelani now & whose military arm is the HeM) .
Now, SA being the unquestioned leader of the Kashmiris could well have fostered the feelings of amity towards the Indian Republic and aided reconciliation and assimilation within it since 1948. Instead, he promoted seccessionism first covertly & then in a semi overt manner thus alienating the populace in Kashmir to the extent that when he was released in 1974 & state elections returned the NC to power, the section headed by the JeI became his singular biggest threat. This opened up a new opportunity for SA who when in Delhi pretended to be their man in Srinagar and in Srinagar pretended to be with the Kashmiris.
That's the Genesis of the Kashmir insurgency and subsequent generations of the Abdullahs & Muftis have all borrowed a leaf from Sheikh Abdullah's playbook.The Hurriyat is just another variation of the Abdullahs & Saeeds family. They're all of one color. It's just the shade of green which is different.