When did the cubicle become the standard in offices throughout the country?
You might find this article about the MOMA exhibit “Workspheres” is relevant.
http://www.cnn.com/2000/CAREER/trends/10/16/moma/index.html
CNN did a video segment about this show, they showed some early Bauhaus-inspired office-unit designs from the late 1930s that were commercial failures but influential, that’s about as early as you can date it. I also saw a Frank Lloyd Wright office unit that is on display at LACMA, they were designed for the Johnson Wax building, but removed during later renovations. These were both key inspirations in office-unit designs. Curse them both!
Anyway, the article claims the cubie boom started in the postwar era when office workers expanded and needed cheap fixtures, and mass-manufacturers were looking for new goods to make.