Fallout New Vegas

It makes a lot more sense for society to rebuild quickly.

The Enclave had the desire to restore their control of the entire continent and a small army of supersoldiers. They may not have had the capability to manufacture more plasma rifles and power armor, but they had the recorded knowledge needed to restore that capability and they were up against small, disorganized, and poorly armed bands of survivors. Maybe they couldn't emerge from their bunkers right away because the surface was uninhabitably radioactive, but survival on the surface became possible long before 200 years had passed.

The games are much more about the rule of cool than realism and that's not a bad thing. I'm just being pedantic.