China is not stupid like Japan was in WW2. China does NOT want a separated India. A separated India is a vulnerable India with a LOT of people. It also has nuclear, biological and chemical weapon that could very easily find itself in the hands of terrorists. A separated India is also not going to be an independent India, this means that other great power (namely the US, UK, France, Russia, Pakistan, and even Japan), will seek to fill the power vacuum, which is very bad for China.
Right now, the subcontinent's balance of power is still quite stable. China can inexpensively exert enough deterrent on India, with the help of Pakistan, Nepal and some times Bangladesh to keep a balance of power in the region. If China somehow breaks India up, then the shared interest between China, Pakistan, Nepal and Bangladesh would be gone. Other great powers will come in, the whole region will become complicated again, and China will be dragged into the conflict.
An India which separates into lots of smaller states looks like a divided squabbling Europe, which outside powers like Russia, China and the USA can influence. But would it be more like Europe in the 19th century, 20th century or the 21st century?
And always remember that China can project more economic and military power onto the Indian subcontinent than anyone else.
I also think you're overestimating the effect of terrorists getting their hands on NBC weapons.
Who are these terrorists? And what is their objective? How easy would it actually be?
Yes, some of the shared interests between China, Pakistan, Nepal and Bangladesh would be gone.
But that's not an issue because India would have disintegrated.
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The other question is the level of friendliness/hostility that India has towards China.
At the moment, the India public and elite are intrinsically hostile to China - much of which has come from the fake media narrative over the last 50+ years, that China launched a surprise unprovoked attack on an innocent India in 1962. If that narrative remains, it is very difficult to work with India.
Just read up on the Brooks-Henderson report on the 1962 war.
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So on balance, I think a divided India would be better from a Chinese perspective.
But actually making this happen isn't worth the huge costs involved.
Unless of course, India becomes an actively hostile state that joins an anti-China alliance.