China, by way of a larger navy and bigger aspirations, has to dedicate naval resources to the pacific to test US influence, maintain a heavy presence in the contested waters of South China Sea - and despite all your grandstanding, most strategists would agree that these are more pressing issues for PLAN. After handling these issues, i would imagine, that PLAN would be stretched too thin to flex muscles in the Indian Ocean.
Besides, with no navy in the subcontinent, competent enough to challenge the Indian navy - India can afford to dedicate a large part of its naval resources for maintaining control over the waters of Indian Ocean. Add to this, the airforce base in andamans, and India has sufficient hardware to deter adventurism by the Chinese.
Despite what you might have been taught, China is no where near launching ambitious plans in the Indian Ocean, especially not with the kind of submarines that give competition to loud mouths, like yourself, in terms of the noise they create.