did everyone want a car because we had such a good road system, or did we build a road system because everyone had a car?
The U.S. built and developed the Interstate Highway system in the 1950's for two major reasons, one was for commerce (and making it easier for it to take place, especially across state lines) and the other (and most argued at the time) was to provide improved mobility for Wartime and Civil Defense use. The American infatuation with the automobile certainly became larger with the completion of this project but it was not the primary reason as to why the U.S. undertook the Interstate Highway project.
President Eisenhower was a huge proponent of developing the interstate highway system to improve interstate travel and commerce specifically due to his experience as an officer shortly after returning from Europe in 1919. He was tasked as a Lieutenant Colonel to lead a transcontinental motor convoy from Washington D.C. to San Francisco and report on road conditions and issues faced by the convoy along the way. It took 62 days to reach San Francisco, due to poor roads (and sometimes no roads at all) and mechanical failure due to various road conditions. This mission is directly attributable to Eisenhower's decision to undertake and fund the Interstate Highway system during his administration.
You can read the convoy report itself as well as Eisenhower's memos on the convoy here, The 1919 Transcontinental Motor Convoy .