Should the US and its allies in the Asia-Pacific region create a "new NATO" to counter China?

[Frodo]

Yes, with Japan, Australia, and India as the three-legged stool of this alliance (with the United States as the primus inter pares, naturally).  And we should consider letting Japan develop nuclear weapons to help protect itself.  

[Frodo]

Yes, with Japan, Australia, and India as the three-legged stool of this alliance (with the United States as the primus inter pares, naturally).  And we should consider letting Japan develop nuclear weapons to help protect itself.  

It's not a matter of "letting" Japan do anything. They simply have no appetite or need for it. The US Navy already provides a nuclear deterrent to balance China and Russia in that neighborhood.

And India is is non-aligned, and will be for the foreseeable future.

An alliance is a process of deepening relationships that take time to develop.  We didn't automatically become an ally of Great Britain, for instance.  Even as we intervened in the First World War (albeit a bit late) on behalf of the Allies, we still regarded Britain as a potential threat in the interwar years.  It wasn't until we entered into the Second World War that we became full-fledged allies, and have remained as such ever since. It doubtless helped that the powers that ruled the British Empire regarded us as a natural successor, and were patient with us as we grew into the role and finally accepted the mantle of world leadership.  

India will get there too (we are already strategic allies of a sort with a common threat), though I do not think it will take quite as long between the initial warming of relations and a full alliance as it did between the United States and Great Britain (which took about forty years).

[Frodo]

An alliance is a process of deepening relationships that take time to develop.  We didn't automatically become an ally of Great Britain, for instance.  Even as we intervened in the First World War (albeit a bit late) on behalf of the Allies, we still regarded Britain as a potential threat in the interwar years.  It wasn't until we entered into the Second World War that we became full-fledged allies. It doubtless helped that the powers that ruled the British Empire regarded us as a natural successor, and were patient with us as we grew into the role and finally accepted the mantle of world leadership.  

India will get there too, though I do not think it will take quite as long between the initial warming of relations and a full alliance as it did between the United States and Great Britain.

It's not about India and the US not getting along, it's about where India sees itself in the world. India's foreign policy goal is achieving supremacy in its own neighborhood (which nobody outside the region cares about) and becoming a great power at the global level.

None of which can be accomplished without our acquiescence or active assistance.  We could not have enforced the Monroe Doctrine without the Royal Navy through the 19th century, for example, until we had built up our own naval strength.  And India cannot achieve supremacy in the Indian Ocean region without the assistance of the US Navy.  And we would only do that if we saw it in our interest for India to achieve its ambitions.  And it just so happens that it is.

These goals don't align with US interests, especially as India is too large, distant, and uninterested to fall into China's sphere of influence.

Yes, they do?  India is the world's largest democracy; China is an autocracy.  As the world's oldest democracy, we want India to counterbalance Chinese hegemonic ambitions in Asia.  So we help India realize its ambitions to accomplish that mission.  

Anything deeper than a very specific alliance of convenience with India (or Pakistan) would require the US to take sides on that issue, which is obviously not in US interests.

If by 'that issue' you are referring to the seventy-year conflict between India and Pakistan since the Partition, we have already pretty much tipped our hand to all and sundry in favor of India.  That bird has flown.  Though we should be encouraging all the countries that once composed British India (I am primarily referring to India, Pakistan, and Bangladesh) to begin the process of reconciliation and eventual reunification.  A united India is more useful and desirable than a divided India.  But we'll work with what we've got.  For the religious divisions that led to the Partition, I will always curse the British...  

Why would India want to join a bunch of losers (every single major ally of the US, with the exception of Israel, is in decline), who have vastly different interests regarding China, when it can continue with an independent foreign policy that works well enough for them?

Because it can't do it alone?  Why do you think India has turned to the United States in the first place?  It cannot confront China by itself -it currently lacks the strength.  And as for our 'declining loser allies' as you put it, they still pack quite a punch, especially when they stand united.  For example, China is still terrified of Japan re-arming despite its less-than-optimal demographic trends.