Why is China still under socialism with Chinese characteristics?

I understand that the market reforms where great for the people of China and helped it develop into a global superpower competing with the USA. However, now that there is such growth, shouldn't they start tuning down the private sector until it's fully replaced? Similar market reforms happened in the USSR, but that was replaced when the USSR economy grew. I tried to research it, but all I got was capitalist bs from the west. Also, even with the private sector, shouldn't higher education be paid for? I understand that there is nuance and it is not that simple, that is why I'm posting this: I want to understand the nuance, not to spread ultra bs.