They don’t own and operate. That’s the way it used to be with roads in the USA for the most part, save in the case of shunpikes and municipal ownership. At the turn of the century, states suddenly started assuming ownership of road networks; one can surmise easily what influenced that.
And it’s also not constitutional to give this to the executive branch to be involved in (the FHWA is a division of the USDOT; note that the executive branch is steadily given more and more power from the start of the twentieth century onwards). The closest thing to any federal involvement is the Postal Clause, which gives Congress the power to create “post roads”, not the executive. The problem is that it is just about exactly the same as how socialistic countries built their highways; their level of control over their own societies is a matter of record, and doing the same here has produced a lot of the same outcomes.