... we are ignoring Pakistan which is the much bigger nuclear threat.

a quasi-ally in its half-assed way,

whereas Iran has committed multiple crazed acts against random westerners, in addition to frequently torturing or gunning down its own people in the streets when they get troublesome.

Pakistan at least keeps up a pretense of being a democracy.

That's my best guess.

ISI trained Lashkar-e-Taiba the group responsible for the Mumbai attacks.

are in thrall to KSA. Which is presumably using it as a convenient nuclear laboratory.
(Of course kSA is also our quasi-ally, so no problem there... And they never ever ever fund terrorism.)

...building nukes?

Nothing has changed. The same power brokers who funded the rise of global terrorism are still calling much of the shots.

India's conventional military forces are superior to Pakistan's. In a conventional war with out nukes India would probably win easily.

on America's completely insane defense budget?

Some countries might look at America's return on that unprecedented investment and want some. Scholars have studied the effects of 2 world wars and the cold war on America's economy. Make no mistake, some people look at war and see dollar signs and start salivating.

To understand what drives Pakistan's policy choices you have to follow the money. Who benefits from the endless India-Pakistan war? Consider the situation inside Pakistan. The Pakistani Army dominates Pakistan, both politically and economically. Army owned enterprises include bakeries, banking, sugar mills, fertilizer factories etc. You can find details at GlobalSecurity (dot) org. The Army officers live in the luxurious houses in fashionable neighborhoods, waited on hand and foot by a multitude of servants.

The Pakistani Army officers are like medieval feudals who lord it over the Pakistani citizens. This of course is to the detriment of the citizens. Now, if Pakistan did not have an external enemy its Army could not justify its power within Pakistan. Hence the Army needs to keep the war with India going. Without India the Pakistani Army would have to answer the question its citizens would inevitably ask "Why do you have all these economic benefits and power, what are you doing for us?" The only answer the Pakistani Army can provide is "our enemy India", so it is essential for the Pakistani Army that India and Pakistan remain enemies.

When Nawaz Sharif (a businessman) came to power in 1997 his attitude was "the Kashmir issue is not of any benefit to Pakistanis, let's instead concentrate on economic development, and for that we need to have better relations with India". Sharif met with Vajpayee in 1999 and signed the Lahore Declaration. For a brief moment it seemed that India and Pakistan could have better relations. However the Pakistani Army responded by starting the Kargil war, and then overthrowing Sharif in a coup. While it secured its own position within Pakistan by doing so, it also meant that the Pakistani citizens went back to the life of serfs under their Army officer lords.

The reason this situation continues is that the average Pakistanis do not realize that the enmity with India is costly for them, instead they continue to passionately believe that India is hostile to Pakistan and the cause of their problems. The truth is that Indians would be ecstatic if there was no enmity, or even if the two countries simply ignored each other. The Kashmir issue is irrelevant, why should India give away Kashmir to Pakistan when Kashmiris have full democratic rights in India whereas in Pakistan they would be serfs of the Pakistani Army officers? Also, if India was to give Kashmir to Pakistan tomorrow the Pakistani Army would quickly come up with some issue to keep the hostility with India going. Then a weakened India (minus Kashmir) would have to face a still belligerent Pakistan. There will be no peace as long as the Pakistani citizens do not realize that India is the only issue the Pakistani Army has for maintaining the position of its officers as the ruling feudal lords of Pakistan.

"...the Pakistani Army responded by starting the Kargil war..."
That is EXACTLY RIGHT. And what it meant (and hopefully no longer means) is that the head of the Pakistani government had no control over starting a war, and no control over the military.

was Nawaz Sharif. About 6 months after the Kargil war he was deposed in a coup by the Pakistani Army and spent a long time in a jail cell.

So you are right when you say "the head of the Pakistani government had no control over starting a war, and no control over the military".

The Pakistani Army loves the Pakistani nukes. It gives them a relevance they cannot otherwise acquire through their inept conventional capabilities.

...as he describes it here:

but they'll do it. They DON'T provide for the people.

Eurasia isn't a Great Game, it's a Nuclear Cluster......

Much more likely that Pakistan will be a molten slab of radioactivity through failed safety.

It's not as if anyone wants them armed with nukes, and it's not like they don't have better things to do with their time and money.