For mortgage and car loans you do not need credit card either.
So we can just give up credit card totally. We do need a new way to build people's credit scores somehow though.
Credit cards only matter to Equifax and other credit scoring companies because of the "instant loan" that they give to a consumer. The banks that issue credit cards want to know if the consumer will pay back that loan.
As long as consumers can get instant loans through some kind of mechanism (credit card, phone, pinky swear, etc.) there will be a role for credit scores and the companies that generate them.
So, just because credit cards aren't common in China, doesn't mean that there isn't some other equivalent tracking going on... (although, I don't know any specifics).
Yes people still need credit, and typically a government branch keeps track this kind of information.
[1] https://www.nytimes.com/2017/09/29/us/puerto-rico-shortages-...