Personally, I doubt whether many Cold War-era missiles would still work. I mean, most materials degrade over time, especially highly reactive rocket fuels and the explosives in the nukes. This is no reason to feel safe though - the newer stuff and the gadgets of the Chinese are in prime condition. And it takes only one of them to open up a whole new chapter of history...
China, unlike the United States, and Russia, has a nuclear arsenal numbering in the hundreds, instead of the thousands. It also has a no-first-use policy For those reason, I trust it to use then in a purely defensive manner.
> There is zero rational reason for that fear disappearing.
Yes, there is. Political bravado coupled with distrust of politics in general and mainstream information being what it is today it's very hard for citizens to notice geo-political turmoils.
Personnaly I'd blame the fascination for useless plastic gadgets masquerading as star-trek level tech but I can't be certain.
They still have thousands of nuclear weapons pointed at eachother, on hairtrigger alert.
There is zero rational reason for that fear disappearing.