I think Uber in this case managed to capture a large demographic of people who do not take taxis, but who are willing to pay for Uber, hence the market for Uber

I think Uber in this case managed to capture a large demographic of people who do not take taxis, but who are willing to pay for Uber, hence the market for Uber in the US is that of $11 billion/year + X billion/year of people who fall in that category. Consider the fact that just last year, Uber had more than $10 billion in transaction (keeping 20% of that as revenue)