This is ludicrously wrong of India, and I understand enough of human nature and economics that I’d be surprised if it were true of China, though it may be more suppressed.
Monetary policy is government policy. The ruling party is seldom uniformly popular across their entire domain. Perhaps you’re more familiar with US politics: broadly, rural is Republican, urban is Democrat. In India, the ruling party BJP has a lot of the north, but not so much of the south or east. Accordingly, you should expect dissent from regions with a different state government. And as for socioeconomic disparity between states, rich may complain if they seem to be subsidising poor, poor may complain if they don’t seem to be getting enough attention.
> Monetary policy is government policy. The ruling party is seldom uniformly popular across their entire domain.
If by monetary policy you are referring to fiscal policy, you're pretty much spot on. There's always in-fighting between states and lots of complaining about the central/federal government favoring certain states over others.
I mean and also the US, but the key difference here is that those are also cohesive countries where wealth transfers between different areas is the norm. Much less problematic if a policy is better for New York than Alabama if you know for sure that the federal government is going to make sure Alabama doesn't get screwed.
In the EU you have the opposite problem: policies that benefit rich countries will result in the rich countries complaining about how they support the other economies and moralizing.
One small disruptor to a core component of a small economy and they are standing outside the IMF to survive.
There are currently 50-60 small countries that depend on borrowing from the IMF (that too in dollars paying interest in dollars - given competition levels guess what dollar generating capacities small economies have? They end up economic vassals of larger systems or selling off national assets or being used in geopolitical games).
On the other hand look at China and India. They have more provinces/states than the EU and larger populations. Vastly differently economies spanning all those subunits. Yet you wont find any of those subunits complaining about their central bank setting monetary policy.
Why? Cuz look at the surroundings - Sri Lanka/Pakistan/Myanmar/Bangladesh/Thailand/Indonesia/even South Korea all at one point or another requiring the IMF to step in and bail them out when they ran into trouble.
The world is too complex and fast/ever changing and small economies are increasingly dependent on larger economies to manage the unknowns and unpredictability that lie ahead. Its almost become impossible to survive by themselves. Sort of like running a book store in the era of Amazon.