Building new, faster roads in rural areas would be outrageously expensive per capita and would rarely be used, there is no economy to justify the expenditure. There are 2.2 million kilometers of unpaved road in the US. Even for the paved rural roads, many of them are relatively low-speed or circuitous because it is cheaper to go around myriad engineering obstacles than through them. It is difficult to justify tunneling 20 kilometers through a mountain range with a high-speed road so that 100 people can shave an hour off getting to the other side of that mountain range where there might be a fast highway.
Helicopters and similar have problems of limited range and operating ceiling, which are particularly relevant in the western US, in addition to requiring safe landing areas that may not be readily available. It is a challenging problem to solve, the US is quite large and many areas where people live are rugged and remote.
I would beg to differ -- the vast majority of rural roads in this country west of Pennsylvania are mile by mile grid, wide, and 55 MPH fast moving. They don't get you anywhere nearly as fast as freeways, they often slow down through tiny hamlets and they have lots of stop signs, but they're already very fast compared to a lot of places.
Edit: Which is to say that I agree with you more than the grandparent.
Those grids are not a problem, they drive relatively fast for unpaved roads, but the grids completely disappear once you reach the mountains in the western third of the US, even in large unbroken crop areas like The Palouse with proper rural roads. Many parts of the South are similar, though in those parts the meandering rural roads are defined more by water obstacles.
The major highways in the rural west, on the other hand, are very fast (90 MPH is normal) once you get to them, but the geographic distances between places that resemble civilization on those highways are often quite large even at that speed.
Helicopters and similar have problems of limited range and operating ceiling, which are particularly relevant in the western US, in addition to requiring safe landing areas that may not be readily available. It is a challenging problem to solve, the US is quite large and many areas where people live are rugged and remote.