N-subs are able to deploy over long distance. You are 100% correct here. But how does that make them harder to hunt? Unless you are using N subs as VIP bunkers to hide from apocalypse, it does not make sense. N-submarines are deployed to fight and hence must have to be in the shipping route which means warships will be able to detect them. Relative to K-subs, N-subs will be much easier to detect due to much higher level of noise and thermals.
I know ASW is not simple. But when compared to N-sub, K-sub has lower signatures and hence have lower probability of detection.
As for 20 billion dollars, a single submarine even in USA does not cost that much. Indian submarines cost high as cost of infrastructure, trainings, industry supply chains etc are involved due to it being a first time project. But subsequent projects will have much lower costs, likely to the tune of 4000 crores. Kalvari submarine without any critical TOT costs 3000 crores even without AIP!
A diesel submarine carries 300tons of diesel for 30 day deployment. This is 10tons per day. Even if a submarine is deployed for 6 months a year, in 20 years, it would consume 40000 tons of diesel which will cost nearly 500 crores in expense of which 50% is forex (oil is imported but diesel has 100% taxation & hence only 50% cost is taken). Also, there is additional cost of fuel cell refuelling etc.
So, it is not cost but feasibility, ease of repair, recovering losses etc that make K-subs so functionally useful for Indian context. This is also why Russia, China, despite their huge resources, still build diesel submarines. They need diesel submarines to deal with nearby shores and littoral waters for marine border defence.
