The ultimate test for a monopoly is if the monopolist could raise prices significantly and not lose significant business to competitors. I don't think Uber could pass that test.
Speaking anecdotally, I know for sure that I'd use a cheaper alternative to save $5 even if it took an extra 10 min.
In many cities Uber is losing money, but in many others they are doing very well. They probably adjust prices to optimize for growth in the cities where they're trying to gain traction. In established cities (as in SF), they tend to raise prices slowly.