What you say is true, and the Constitution does empower the Federal government to build “post roads”. But we got along nicely without a Department of Transportation until about 1965.
I am just a few ticks north of US 40, the old National Road, which was the first highway built and financed by the US Government.
There was a lengthy, spirited and protracted fight in Congress at the time over whether or not this was the proper role of government. It passed narrowly.