US also need to counter india's military growth in south asia. So, US would like to have india's help on countaining China doesn't mean it wants to give india's free hand in south aisa by forming an alliance. If you look at US' history of aiding Pak before 911, you would realise that Pak has been US' important ally in south asia which is aiming at --- India.
Before you ask that, you should ask yourself a question: did US or Russia want to form such alliance?
Of course both of them want to counter Chinese military growth, but that doesn't mean they need an alliance with India by bearing some obligations for india.
To Russia, they have to consider their relationship with China on economy, political and military. They can't get more from alliance than their current policy.
In the case of US, they want to counter China in Asia but they also want to counter india's growing influence in south Asia in the meantime.
Your assertion that USA will also like to counter India's military growth in South Asia is based on flawed assumption if there is any in your mind.
If that is the case why would they be willing to sell the latest in military weapons and refuse to sell the same to China? Pakistan's alliance has not paid any dividend from the stability of the Pakistan nation itself and in the neighbourhood as well since they are playing to the tunes of your esteemed CCP and PLA ideology of containing India, which has started to backfire in itself and left your regime in quandrum that is why your Government keeps issuing verbal warning to India on SCC issue. Besides times have changed in the economic sector of the region. The nations other than Pakistan in Asia are more lucrative to the business titans of USA than Pakistan. All you have to do is put all the number of USA exports to countries of S.E. Asia and South Asia and in the other column Dollar figures on USA export to Pakistan, anybody with a common sense will come to same judgement that time has come for USA to move on.
What I read into your assumption is fear that CCP and PLA is experiencing due to the possibilities of trilateral alliance which might be formed in the near future. Who is at fault that is the question you have to figure out. I know the answer already. Russia already has a military alliance with India if I remember correctly it was started durin the Indian and Pakistan war of 1971.
The leadership and common citizen of these two countries has a different take on alliance with India than what you think. India will not be burden on their economy but economic benefit to both of them as compared to Pakistan. Your only problem is the goals of your ruling thugs will not be realised at all ever in the future millennium and that is the giving you sleepless nights.
Now let us look at Russia. Are you saying that Russia has more to gain from China in the economy, political and military? How can you explain in detail rather than one line answer? From what I know Russia's major export to China is natural gas and oil. They can export the same commodity to Europe and other Asian countries. I do not see the political gain to Russia. Military, I do not think your country would dare to take on Russia. You do not want to wake up sleeping but alert Bear. If any one of your leader do that it will be the biggest strategic mistake for your nation. This will give you four enemies on four sides of your border. If you do not know let me know, I will tell you.
In Asia region USA does want a strong military counter weight to China to contain ever aggressive nation of yours towards all the neighbours in the region. You keep claiming Arunachal Pradesh state of India, SCC reefs, islets from Vietnam, Philippines. You are also claiming Leodo reefs of the Island of Jeju from North Korea in the latest development. Thus you are going to push North Korea towards South Korea and it has been done in the past by your regime.
USA does see India as a natural ally, which has had a peaceful coexistence with her neighbours ever since the Independence in 1947. India also provides an economic clout and exchange of goods and services both ways which no other democratic and transparent economy in Asia does. Now do not come back to claim that China provides the same benefits to USA and Western as India does. It does not when it comes to transparency and openness of the market. Do your own research if you want to satisfy your mind.
USA and Russia do not look at India as a threat militarily or economically but as an equal partner that is why their defense industries see no problem in joint collaboration projects or transfer of technology. Where as China has become a headache due to counterfeiting of products and not enforcing the WTO rules.