Why should the federal government be responsible for roads and bridges? Even if Fedzilla was somehow, someway kept small and lean, they’d still hold that over every state’s head, keeping billions from them.
Unfortunately, more politicians wanted the feds to get their hand in that pie. It's been downhill ever since.
There are some things that just wouldn't be provided without the public sector. The earliest private road (sometime in the 1700's) was what is now known as the Pennsylvania Turnpike. Back then, it was a "corduroy road" made up of split logs. When you reached a certain point, there was a small hut with a long stick (i.e., a "pike") across the road to stop you. You paid the toll and the pike was lifted (turnpike). It didn't take long for users to build little shortcuts around the turnpikes. Without revenues, the roads fell into disrepair and commerce suffered (especially in the wet seasons).
In Boston, you can still see private homes with a fire company name on them in the form of a plaque. If there was a fire, you read the plaque on the house and ran to that fire house. Heaven help you if the plaque was destroyed or otherwise missing when a fire broke out. In this case, duplication of services made a natural gov't-provided monopoly more sensible.
There are plenty of other places to get rid of long before you remove the road system.
In 1918 railroads were how people and freight traveled across the country. That year Dwight Eisenhower was a junior officer in an operation designed to see if it was possible to get a motorized convoy across the country.
There was very little paved road. There were very few maps for the primitive roads that did exist. It was a long and arduous trip. This trip was the genesis of the Interstate Highway System built during his presidency.