That argument played out in the early 1800s. The first National Road was authorized by Congress in 1802 and constructed from 1811 through the 1830s.
That matter was a subject of great dispute in the U.S. government at the time -- for the reasons you have laid out about the limits of federal power.
There's a reason why the "Federalist" view won the day, and the timing of that first federal appropriation for the National Road had everything to do with it. If you look at a map of the original thirteen states and you review the history of the colonies, you'll see two obvious historical and geographical points that informed the founders' views on transportation infrastructure when they drafted the Constitition:
1. Every one of the original thirteen states was located on the Atlantic seaboard.
2. There was already a network of government-owned roads in place in these thirteen states from the time of British colonial rule. These "king's roads" became the "post roads" that are cited in the U.S. Constitution under the enumerated powers of the federal governments.
Most commerce between the original states took place via marine shipping or along these "post roads." If the U.S. never grew beyond these 13 states, nothing ever would have needed to change.
The conversations about building a national road system beyond these original "post roads" began very soon after the Constitution was ratified. With the admission of Vermont (1791), Kentucky (1792) and Tennessee (1796), the U.S. now had sovereign states within its borders that did NOT have direct access to Atlantic ports. There wasn't much urgency in addressing this, however, since these three states were very rural and encompassed lands that had previously been subject to claims among one or more of the original 13 states. So their limitations were well established and understood by everyone at the time.
It was the admission of Ohio into the Union in 1803 that brought the whole question to a head in Congress. Under a strict interpretation of the Constitution, the U.S. government might have had no authority to construct a new road between states. However, the powers at the time -- including Thomas Jefferson himself, who was very much a champion of state's rights -- recognized that every new state admitted to the Union that lay west of the Appalachian Mountains would have limited ties to the rest of the U.S. unless they could maintain and grow commerce throughout the nation without being subject to the whims of their neighboring states when it came to the construction and maintenance of roadways.
That original National Road was established to run west from Cumberland, Maryland across a route that is now roughly followed by I-70 and Route US-40. It was considered a "no brainer" at the time because without such a road in place, the Northwest Territory -- which included a large region in the interior of North America that later became Ohio, Michigan, Indiana, Illinois, Wisconsin, and part of Minnesota -- would have closer commercial ties to British Canada than to the rest of the United States.
So there you have the REST of the story ...
There was great resistance to national roads in the south whose leaders saw it as spending their tax dollars for northern interests. South had a large system of navigable rivers and with the Louisiana Purchase the port of New Orleans became the center of trade for the interior southern states. Similarly a system of navigable rivers flowed east from the Appalachians to the Atlantic facilitating Southern transport to the Atlantic coast.