Uhh, no. Just no. The history of religion (and politics for that matter) in Asia is entirely more complex than your characterization suggests. ...
Korea ...
Japan has primarily a mix of Mahayana Buddhist and Shinto, ...
India has had the Vedic traditions for thousands of years. Buddhism can be ... ethnicity, etc.
So people here start to discuss about other religions finally.
From my perspective, I assume all religious believes are subjective views of a certain category ideas/believes, hence everyone has one's own 'sub-religion'. Like all creatures are different, since there are so many possibilities of combinations of believes and ideas can exist. So if you group people together by similarity in common believes and ideas, you get bigger and bigger mother groups which share less and less common traits, until there are just few groups left and each defined by some few significant common ideologies.
On the other hands, you can also trace the origin of someone's believes through time, and find out where is certain ideologies originated from. And if possible, you may trace them back to certain ancient groups of people who started these common trade of ideologies (religion founders and their followers). And one can measure the similarities of traits between the existing mother groups and the traits with those historical ones. Thus we can truly calculate how much influence each current religious groups affects each other, and how many traits stay true to the origins. But I believed it will be a difficult subject, since the history of religion are often clouded, and measuring and defining certain ideas within people's heads may prove difficult. (meme? I still very confused about how to define a meme.) Maybe if this method can be done in some ways, can we truly objectively discuss what's the difference of each religion. And why they spread so unevenly.
I thought religions are like creatures competing the space of limited resources - human brains (Very Dawkins thoughts). And a dense populated area like China, India, will be good breading grounds for them. Will they eating and merging with each others? Or eliminated other competitors by killing the host? Or removing the old ones placing with new ones (conversion)?
About the diversities, I think the population of japan, Korea, are relatively few compare to the whole population of East Asia. And the diversity in these fracture lands and their diversity in religions, exactly proving my points rather than disproving it. And the phenomena like people practicing these fundamentally different religions (Buddhism/Taoism/Confucianism) with mashup style in their life, should also mean in the mind of general populations they are not seen as separated ideologies but rather integrated. Many temples (truly for general populations than the ones for monks/nuns) in China and their offshoots (Taoists seems more acceptable to other believes), you can see Confucian Figures (Mostly historical figures and later viewed as Deities), siting on the side of Taoist Deities (Many many of them, mostly fictional), along with statues of Buddha, but mostly Bodhisattvas, and Vajra. So people can pray to all of them without traveling long distance to different temples. Isn't that the definition of merges in believes? You don't see a church who prey to Allah, or a Mosque decorated with saints and angels, or a Judaist prays to Jesus. They don't mashup like we do in the Far East. That's what I thought it's because the nature of monotheism causing this, or is it the culture difference? Or is it political? I don't know. And my assumptions are fairly rudimentary. But if there is a trend, then why? Can we study them? (I still confused with India, they are between the boarders of monotheism, but majority are Hindu over 80%. That's a lot unity than difference.)