When India gets her 12 nuclear submarines, it means her navy power and air force must be at least reaching the level of China of today. In other words, when this time comes, India will be in the same position as China today - a challenger to US's dominance in a region, it will be IOR in India's case.
It is not how India wants, it is what India need: for example, India need to secure her oil supply from middle east. Then India needs to build stable relationship with some of oil supply countries (i.e Iran or Saudi Arab). This relationship means you need to come to help when they are in trouble with other powers (i.e US). When you are doing that, no matter what you think, from US perspective, you are damaging her influence. Certainly you become another challenger.
No it is important for any power, especially IOR.
IOR is a specially region, it is the next to middle east - world oil center and then Europe; going north, it is central asia; going south west, it is Africa; going east, it is South east Asia. So, IOR is actually a door to 3 major parts of the worlds. Strategically, a country controlling IOR can easily projects her power over Europe, Africa, Asia. If India becomes a dominance power in IOR, you could say it will naturally become a world power overnight. And it is much harder and more dangerous to check such a power than China or US. It will be a nightmare for any power outside the region.
USA was alarmed when Chinese economic scale reach 50% of hers ($10T). In the case of India, the benchmark will be much lower (maybe $7-8T). So, the only way that India can be US's ally is India keep herself under around 40% of USA's economic strength. Is India willing to compromise on this? I don't think so.