There was no need for the executive branch to build it (its Bureau of Public Roads had its powers increased for this self-appointed task by an all-too-willing Congress). The private sector would have been more than up to the task.
The private railroads proved by helping to win WWII that Wilson was absolutely wrong to nationalize them in WWI.
And what with Eisenhower inspired by the Reichsautobahn, perhaps he forgot that those roads made things easier for the Allies to get to Berlin? Strategically problematic to introduce the same vulnerability to the home front.
We are protected on two sides by oceans. No foreign power is ever going to come to our shores and invade us from there (exploiting our highway system).
(Please: No cheap jokes about the invasion already taking place along the Mexican border!)
Regards,