Malaysia is stuck in the middle income trap. As for China, because of the hukou, a huge chunk of the population is not allowed to access high quality services in cities. That's why both countries have lower than expected HDI.
As I mentioned, since the private sector is the reason why India's HDI is higher than normal, access to cities is important for migrant families. In India, we allow unlimited immigration into cities, that's why our urbanization is pretty high for our level of per capita and agrarian labour.
Take a look at India's per capita and compare that to countries around India.
https://en.wikipedia.org/wiki/List_of_countries_by_GDP_(nominal)_per_capita
India is at the same level as Ghana, BD, Pakistan, Congo etc in terms of per capita income, but they all have much, much lower HDI than India does. And this is with a population that's over a billion.
If China had allowed unlimited access to cities, then China's HDI would have been much higher than it is today. Not to mention, a lot of money and manpower was used up in the management of the failed one-child policy.
China was politically aligned with the West and attracted huge investments and technology while India was politically aligned with the USSR and attracted nothing. So this played a huge part in the slower development of India even after the USSR disintegrated. The USSR propped up and kept India weak by encouraging bad socialist policies so that India doesn't become a thorn in their sides in the future due to our democratic principles. The huge influx of capital from the West helped China improve HDI rapidly, the same wasn't possible in India.
India's HDI is also growing according to the law of diminishing returns, but we haven't even reached our fastest pace yet. You forget that we will be massively improving our HDI with a growing population while most other countries already had declining populations while they transitioned to higher HDI. Even after we cross 0.9, our population will still be growing. This is what's called demographic dividend.
So China's tightly controlled high end govt services shouldn't be compared with India's loosely controlled high end private services. India has crawled and stumbled itself towards its current level of development. Now, you can watch as we run towards our next goal.