The insanity that is Uber - a 100$B company?

So we've had taxis for years and we know that generally taxi drivers work hard, long hours and make small amounts of money. The cab companies make more, of course, but I don't think there are a whole lot of billionaires in the taxi business.

And now there is Uber. An earlier round of VC $ put its value at $17B. According to Fortune, Uber is now "raising new funding at a valuation of between $35 billion and $40 billion, according to a new report from Bloomberg. This would be one of the richest “venture capital” rounds in history (Facebook still holds the crown), and likely mean that investors expect Uber to eventually go public at a valuation of at least $100 billion."
How are to make any sense of this? Where would all the money come from to make all these investors (and shareholders) rich? 
By cutting out the "middleman" (regulation to ensure safe rides, primarily)? Maybe, but I can't imagine it will generate that much revenue?
By reducing the cost of a ride, compared to a taxi? That's true, apparently, some of the time with Uber, but often it is way MORE expensive - because prices are "market-driven."
By shifting more and more of the costs and risks to the drivers? That's pretty darn likely. Just look at the poor "contractors" who have to pay for their trucks and lease their gear from FedEx. 
By shifting riders from mass transit to Uber (in other greatly expanding the "pie" of pay-per-ride)? Again, that seems unlikely.
What am I missing? How could Uber replace an existing business that brings in nowhere near that much money and suddenly be printing the stuff?
Oh, and that's if they don't self-destruct due to their cavalier, arrogant attitudes and actions of their management.