If you are really sadistic, you don’t really need to glass major cities to collapse nations. If you study a map and look at how many nukes it would take to irradiate the vast majority of the drinking water of the world’s biggest countries, the number might be a lot lower than you think.
I also find all the peepee measuring contest with warhead numbers juvenile and largely irrelevant. It’s not how many warheads you have that matter, but rather how many and how reliably you can delivery them on target. The latter is where China’s nuclear modernisation focus lies, and for good reason. It doesn’t matter if you have a thousand warheads in storage if you cannot hit the enemy with any of them.
That’s not to say 300 warheads is enough for a country like China. But I think that 300 number was always just something someone pulled out of their ass in terms of a ballpark estimate and has never been seriously updated since it served the interests of both sides.