but how can the same system be made to work in areas with large distances between individual users

You can also just look at history to see how this would work. Interurban cars (electric streetcars that are capable of sustaining speeds of 60+mph) would operate on flagstop routes, only stopping at stations if either a passenger onboard requested or a passenger at the station flagged them down. Additionally passengers could often flag the cars from anywhere along the tracks to pick them up (this would vary by system/line)

Combine such a system with bicycles and you're already most of the way there to car-free/car-light rural living