The requirement to ID yourself online was already a thing in China, and using government-provided unique IDs for that isn't the worst way to go about it. The main issue would be mandatory reporting (i.e. if the companies have to constantly send data about what every given ID is doing on their website), but that's a different issue - and I don't feel like it's harder to do this using the phone numbers they already use compared to using a government GUID.
The main issue is that this would make obtaining access to Chinese websites even more difficult for people outside of China. It was kind of possible to go around the phone number restriction by obtaining a phone number, but going around the government ID is going to be significantly more difficult.