If your goal is simply to destroy a country as a functioning power you don’t need to kill every single person. Nuke a handful of major ports and you massively harm the US economy without killing that many people. Add major cities and things get really bad at even a dozen nukes. Sure, we would nuke the fuck out of anyone that launched such an attack but that doesn’t allow us to ignore such attacks.
My point was just that the logic of having only a few nukes while everyone else has many more doesn't work. China has 145 cities that have more than 1 million people. You wouldn't be a serious threat to their industrial base with only a few nukes, and so the effect of your deterrence would be minimal.
Suzhou is next to Shanghai and you devastate them both with a single nuke. https://en.wikipedia.org/wiki/Suzhou
My guess is an 10MT H-bomb could kill ~20 million people by aiming at Suzhou despite the city only having 6.7 million people. Honestly to cripple China with minimal nukes 2-3 Starfish Prime style Nuclear electromagnetic pulses could disable most of their east coast before you target individual cities.
Also, responding in kind to a limited nuclear exchange may be appropriate if you think an adversary still has a large stockpile. There is a lot of uncertainty involved.
Nukemap, known to lots of people here, can help you explore your predictions. Here, I airburst a B-83 over Shanghai so you don't have to: https://nuclearsecrecy.com/nukemap/?&kt=1200&lat=31.2322758&...
Sleep tight...
Hard to say what hypothetical countries arsenals actually look like. The B-41 was supposedly 5.2 megatons of TNT per tonne of bomb designed in the late 1950’s. At 5 tons each a non reusable falcon 9 could get ~4 different 25 Mt bombs to LEO and possibly more on a ballistic trajectory. So it’s not like monsters don’t fit on rockets, saturation bombing is just more effective.