They seem to scale in reverse. That is, an Uber that runs in the US and the UK will cost more to operate than an Uber that runs in just the US. An Uber that runs in one state will cost less than an Uber that runs in a whole country, and so on. The more diverse an area you serve, the more legislation and markets you have to deal with, more hours you'll have high customer support load, and the less well you will be able to analyze and react to trends in individual markets.
What stops me, then, in an era where Uber isn't fueled by investor money every trip, from being a competitor with Uber? Raise a few million dollars, get a simple app together with a few friends, and then convince drivers to try (take a lot of short Uber rides and pitch good drivers) and riders to ride. I'd have less staff, less overhead, and therefore less costs. The savings could be passed on equally to the drivers and riders. I could give discounts on nights when there was a big game, I could advertise in local areas, I could poach good drivers from Uber, etc.
It seems to me there is no way for Uber to be competitive if they aren't using investor to subsidize the price of rides. There is nothing, that I am aware of, that is impossible or expensive to replicate in their tech.