If you haven't discovered the problems with this model, then it's only because not enough of your neighbours have had the same idea.
Look around at places with very high car use (especially in North America) and you'll discover that this solution simply does not scale. Cars take up a gigantic amount of room on roads, and even gigantic highways like Onatrio's 401 [1] just have not been able to keep up with the level of sprawl that occurs when people move out of the city to surrounding suburbs and commute into the city by car.
Adding lanes to the highway does not help and just induces more traffic on it, and it also causes all the surrounding villages to sprawl outwards until they become indistinct blobs that merge into the nearby metropolitan city.
Trains are a much better solution to this problem because they have way better throughput, don't destroy cities with massive highways and parking garages, and encourage denser development that lets nearby villages retain their character and size.