Not necessary. It would simply be a stupid waste of resources. China don't really have liabilities like key allies (in hostile geopolitical situation) or oversea bases that needs nuclear umbrella protection. What's the point of a nuclear arms race with the USA, when China could simply invest in much more important stuff like infrastructure, education, research, conventional military forces, etc.
As long as there is the Russia nuclear arms existing to balance the USA, there are no point for China to have more than 1000 nuclear warheads. As long as China has the necessary effective nuclear deterrence, China would be fine. As long as China has enough missile armed with warheads that will land in the US or Russia, it will be enough.
If US nuked China's nuclear forces, and took out incoming Chinese missiles, China would simply nuke Russia. and Russia will nuke the rest of the world. Russian nuclear forces is already strategically neutralizing the US nuclear advantage.
As long as China has enough nuclear second strike capability to high major centers in either US or Russia, the deterrence is enough.