The argument that "Uber isn't taking the money, but the driver is" seems like a difficult one to make (and I know that you are not making this argument) given that :

a) Uber actually collects the payment and then disburses some payment to the drivers. The amount paid to driver is variable over time as percentage of revenue.

b) Uber's model is not subscription based or something that clearly decouples Uber's revenue from the driver's revenue.

c) Uber initially subsidizes and pays drivers above and beyond the total market revenue to build liquidity.

So, in every possible way Uber's revenue is intertwined with the driver's payment.