What is the purpose of the northernmost roads (where north is the top of the picture)
To my understanding, the last two road segments open up no new territory. Indeed, there should never be a reason to build a road on the outskirts of the map.
They don't appear to serve any purpose, but on the other hand, the Hotel at the top most far left (above the church) appears to be placed without a road, and if I remember correctly, that is not allowed. Only ranches and mines.