Re: I'm not sure I see how they get to profitability
One thing you seem to be missing in your figures is that when individuals drive their own cars for Uber, they voluntarily choose what they feel is the smallest slice of the pie they will tolerate. If pickings are too slim, they hang up for the day/night. There will normally be an excess of cars available before this point, and there will typically be a car nearby.
If Uber are taking all of the profit, and not having to share it with the meatsack in the driver's seat, they can change that threshold. Put fewer cars on the road. So first of all you've saved in capital investment there. Then, because there are fewer cars, the price can be a bit higher, increasing the pool of money. Finally, they're not just taking that 20%. They're grabbing the whole pie and paying off their energy / maintenance before keeping the rest.
I'm not saying that you're wrong. I simply don't know. All I'm saying is that these factors will sway the result quite hard.