A nukes primary target is heavily inhabited cities mainly, so if you wipe out the most population = Less Resistance
I am not sure if nuclear theory in relation to an invasion is the same in the FO universe as it was IRL, but if so, you are incorrect.
If a nuclear war had happened, the vast majority of nuclear weapons fired would
not be aimed at cities. Military bases,
important infrastructure, communication centers, and America's own missile sites were the primary targets for the Soviets
if their intention was then to invade. Knocking out the cities doesn't help you at all if the enemy can do the same to you.
That is why most missile defense systems when they were being developed were planned to be deployed around our own nuclear silos
and military bases. You were safer, for example, in Pittsburgh than you were in Cheyenne or Colorado Springs.
Now, some cities would be targeted due to their vital role in the nation's transportation and communication. Atlanta and Kansas City would
be directly targeted. Many other cities would be heavily damaged as military bases are very close by, but by and large, if you live in a non-important
big city, you'd be saved from the initial attack.
MAD is what stops this from happening, but ths above is not MAD. Now, nuclear theory could be different in the FOverse, but where it
is a reality in the real world, the goal of a nationstate that wishes to invade another with the aid of nuclear weapons is not the destruction
of urban areas for the sake of resistance purposes.