Realistically, the two groups don't need each other. Shia currently are enjoying being an independent sect which is trying to assume leadership of Muslims in the region even though they're the minority. Sunni's also wouldn't need Shia for anything if they become more active about observing the right path of Islam while also valuing education and developing their nations. Right now, however, they have a way to go. But, realistically, these two denominations also need to learn to revolve some differences for greater good of region. So you're right it's not for sake of Israel but for sake of themselves.
To me as I've said number one priority should be observing Islam and worshipping our Lord. And worship has many forms, most of which people don't emphasize anymore. Many acts in ones life that doesn't consist of actual prayer can be considered as worship by God depending on ones intentions. And even if they don't intend it, God will still accept it as that. Regarding Israel, lifting injustice of Israeli's off Palestinians is considered a form of worship to God. And God will write that off in a later time for people who's intentions were pure and people whom he wants to accept that act of worship from them. It should be just considered a side task for those whom it will concern. Main priority and objective Islam (besides our natural aims such as development/education/etc...) is worship of God. And we have to look inwards as there is tons of work/effort to remove corruption, hypocrisy, oppression, and other obstacles plaguing Muslim world that we have to fix in order for God to accept our worship.
God is merciful so I assume he is accepting prayers of all Muslim individuals. But, as a collective group I have doubts he is accepting some of our prayers and wishes. Simply because our societies are not reflective of what an Islamic society should be like. And I don't mean enforcing stricter measures or making everyone wear hijab or what not. We already have some countries with strict measures just for show or just for the government to achieve legitimacy. But, reality is there is much oppression and corruption in our nation's that much of the populations are enabling. There is little to no sincere people in positions of influence, whether in government or scholarly boards, Universities, media, etc.... And that is anti thesis to worshipping God. There have to be good people in these positions who will uphold justice, tackle corruption, tackle hypocrisy which is a big problem in which Muslim factions, political parties, etc... are exploiting Islam in a way to suit them, strictly for power/wealth and so on. If that happens it's a crucial form of worship towards God, and God will indeed accept our initiative we take towards him and bless us and our prayers will bear fruit.
From there we can tackle injustices on different levels. Which will be side tasks or other forms of worship after we look inward and fix ourselves and make it important to worship the Lord. This is all without the need to form any Caliphate. We will still have our different nations/cultures which is fine. The problem is in the distance we've created between us and God which has made us just like any other corrupt nation but IMO even more pathetic than what I've seen in the past.
The way I see is Kashmir is that ongoing events on a weekly basis suggest the Kashmiri's don't want to be under Indian rule and want to be independent. And this is something they should get, if people valued justice in this world. Including the Muslim people who likewise have lots of work to create a just society.
I am glad that Pakistan can in some ways support the population of Kashmir with humanitarian means and it also gives them mental support that someone is behind them. They should work together on the diplomatic front to bring up this issue as well. Which I'm positive is already happening and has been tried throughout time. The Kashmiri's need to continue to persevere for now.