Nuclear weapons are for deterrence, not use. If the other side doesn't know you have thousands of bombs, you might as well not have them. If China already has more than a few hundred nukes, it should be made obvious to the Americans
Similar mindset:
Look, China doesn't need to announce the number of nuclear warheads they have. Announcing the number would definitely cause alarm bells to ring around China's neighbours, especially the likes of Japan and India. This could even kickstart a nuclear arms race around China's vicinity and nullifying China's MAD advantage over all her neighbours (bar Russia).
What China should do instead, is to:
1. Pump out ICBM TEL launchers,
2. Pump out VLO strategic bombers in greater numbers,
3. Pump out SSBNs in greater numbers,
4. Keep expanding those ICBM silo fields in the northwest,
5. Keep expanding the number (and perhaps size as well) of ICBM TEL brigades, and
6. Keep expanding the Underground Great Wall network.
(Of course, while secretly expanding their nuclear warhead count as well).
Individual nuclear warheads can be hidden underground and kept beyond the reach of public eyes and overflying satellites, but the number of launch facilities, ICBM brigade bases, bomber-based air bases and submarine bases will cannot be hidden from overflying satellites, if not from the public eye.
The idea is to keep the Pentagon and White House guessing the exact number of China's nuclear warheads, but letting them have a rough idea on the size of China's nuclear arsenal. Doing the above is enough to send a stern message to the warhawk policy-makers and decision-makers in Washington DC, which is sufficient to keep them in line and not attempt anything stupid against China.
