Uber doesn't offer service in much of the rural US now. There's a ride service specifically for rural areas called Liberty:
http://libertymobilitynow.com/
But even these are for micropolitan areas with populations on the order of 40,000. There is still no service for more remote areas.
WRT "made worse by distances" Bay Area is actually pretty sprawling itself. I don't think any rural community will have its points of interests further apart than Bay Area has.