No one has mentioned that the primary purpose of the interstate highway system when built was national defense.
The history of national highways goes way back before the Federal Highway Aid Act of 1956 that established the U.S. interstate highway system. The first national road was legislated into existence all the way back in the early years of the 19th century.
I think Ike was tasked to take military equipment across the country when he was Lt or Major. The conditions of the roads or lack thereof led him to propose an national Hwy system as you said for defense.