The atomic bombs detonated in 1945 had the blast yield of about 22 kiltons of TNT, the blast yield of the Tsar Bomba(detonated in 1961) was about 50 megatons of TNT. That is our history, in the Fallout history with tension of nuclear war much higher, I'm guessing that China would be stockpiling thousands of nuclear warheads. The Great War occurred over 100 years after the largest man made bomb ever detonated, the constant threat of nuclear war would have seen larger bombs. Besides nukes aren't detonated in the atmosphere, a standard air burst can occur from several hundred to a few thousand feet in the air.
I'm not really understanding why you are trying to defend Bethesda's poor world design.
And the Tsara Bomb is not practical. The bomb in Megaton, sure looks like a gravity bomb to me.
Point is, this is !SCIENCE!, and we have no idea about the Chinese nuclear capabilities, or what the bulk of their bombs consisted of. These bombs could be anywhere from 1-500 kilotons.
Also, pretty sure bombs can be detonated in atmosphere, if you want to take out enemy satellites. But, again, also pretty sure as you stated, you can get different results depending how high off the ground the detonation occurs.
Anyway, the divergence occurred in the 50s. We have no idea what these bombs were like.
However, I'm still wondering, was the crater at the white house the only seen evidence of a surface impact? I can't remember.