1965 is also just as debatable as misadventure as Kargil, to be fair.
Whose Constitutional authority is it to decide on initiating a war? How did this military operation serve Pakistan's national interest in the short and the long term? Is Pakistan closer to getting its way over Kashmir after the Kargil episode?
Please note that there was no LoC demarcated that could be crossed from the last demarcated point except as "thence north to the glaciers" and that is why India stopped at the Saltoro Ridge. That is why Pakistan has never taken the required steps to show a violation of the LoC over this matter.
This drawing room talk of exerting military pressure across the LoC from time to time is merely to ensure the ongoing nature of Pakistan as a security dominated state, that is all, with everlasting damage to its social development. Kashmir the princely state that existed in 1947 has long since been divvied up between three neighboring nuclear powers and there can be no going back to that for the foreseeable future.
India can do as it wishes over this matter is because it has not allowed itself to become a security state and concentrated on its economy for the last few decades, pure and simple. Pakistan, sadly has made the exact opposite choices and the consequences are only just becoming evident, very predictably so, I might add.
If Pakistan wants to achieve the same international gravitas, it must also follow the same strategy of economic and social development and give it a few decades as there are no shortcuts.
In the meantime, there will never been a fruitful outcome to any military misadventures across the LoC, by either side.
But isn't it ironic how all the "right reasons" have given always rise to all the wrong outcomes we see today?
What you propose will never have the right outcomes either because things don't happen sequentially i.e. fix economy and then fix other things. Things have to be tackled as they come. What you are voicing is essentially the in-vogue argument in the camp that suggests let's talk peace with India etc. and let's just fix the economy and everything will work out. It does not work that way.
Secondly, it is not the Pakistani armed forces that are perpetuating the Kashmir conflict so they can keep Pakistan a "security dominated state" as you stated. There is an occupation of a predominantly Muslim people in a UN designated disputed territory that has a lot of emotional and ideological impact on the entire Pakistani nation and this issue remains front and center in the Pakistani psyche. The military is just a microcosm of this same phenomena.
This claim about Pakistan being a security state has been propagated for years now by Pakistan's antagonists and it boils down to a baseless claim that since keeping security issues alive retains the military's importance (and the ability to keep its budget), it is in the interest of the Pakistani military to perpetuate conflict (Military Inc. et-al).
I don't buy this argument.
When we talk about the military-industrial complex in nations where security is considered paramount, Pakistan isn't an exception and also Pakistan is nowhere close to being a security state in the same mold as some of the countries for which the term was coined.
We have a neighbor that spends $50B on arms. Its military has ALL the reasons to perpetuate this funding and it does so by ensuring that its talk of a two-front war scenario allows it the funding it needs. Yes they have a facade of an elected government on their heads, but what we have seen clearly is that they maintain and exercise the veto (e.g. Siachen and Sir Creek etc.) as and when they need. The same goes on in the US where no US foreign policy decision concerning US security goes without guidance and input from the US security apparatus. One can state that Pakistan has had military rule, yes Pakistan did but the military isn't lurking behind the shadows all the time either. If anything, since Musharraf's departure, the military has had a benign role and has gone along with everything that the government of the day has asked of it.
Of course we have specific security compulsions created out of the Kashmir conflict. However Chinese, Indians all have similar compulsions and nobody questions their reasons to fund their military as we do ourselves blindly and in many cases, idiotically based on the hearsay from outsiders.
I recall an interview with Gen. Tariq Khan (Commander, Southern Command) after he had retired. And he gave a lot of examples where the Fed/local government had left their responsibilities in the no-man's land and then asked the military to handle it. The point being this is where the outside critique comes in where they say the PakMil has an outsized role in the Pakistani life. However the answer is, its because our other institutes don't step up to do what they are supposed to and cede space to the military and when the military finds a vacuum, it will try to fill it, sometimes effectively and others not so much.
To your point about sitting quietly till economy is "better", there is no one even within the military who questions the need to grow the economy. It is obvious but it is also not the military that is getting in the way.
Lastly, I disagree that "India can do as it wishes". I don't think this as simple as that and coming months and years will show this won't be the case regardless of what the Indians or their supporters say.