I'm not really sure about that. Maybe I've watched Dr. Strangelove too many times, but everyone knows that flinging all of your nukes at someone kills you too

I'm not really sure about that. Maybe I've watched Dr. Strangelove too many times, but everyone knows that flinging all of your nukes at someone kills you too (the "Doomsday Device"), so what I'd expect to see in WWIII is two things: 1) the clash of a ton of new technologies where we have really no idea what beats what, and 2) strategic, low-yield nukes used against blue-water navies and ports.