Why won't Uber exist in rural areas? And by "rural" I actually mean most of places which aren't a booming megapolis, including cities of ~100,000.

You have a strange definition of rural.

Anyway, out here in the middle of nowhere, Uber, taxi and (high frequency) bus service are not economically viable. Low population means low numbers of fares means low suppliers means long delays for service means lower numbers of fares. All of which is made worse by distances.

Medium and large cities do have taxi service and public transport, but those are lower priority since everyone has a car.

I don't see how Uber would not be unviable anywhere. As a driver, even if you have one rider per month, why not make an extra $10?

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.

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.

Let's say you're on Hartz IV. The $10 have to be accounted for at the social security system, and if you earn to many of them $10's, you don't get to keep them.