I think the schools and other public places are just built around the center of it's surrounding population so it can serve everyone best - since everyone is already spread out in rural areas, the schools have to do their best to accommodate the most households they can so that no child is without education. I couldn't find anything about what happens if a school isn't available for someone that building a house in the middle of nowhere, but I imagine state education departments have to make an effort to service all households with public school.