It's based on total operating costs--not the cost of the driver only. If you include how much they have to pay for everything else (developers, management, advertising, etc), the "cut" they get from each fare is less than how much they spent in other areas. (I could be wrong so please do correct me if so but I believe this is the case here).

Scale only helps if you have high fixed costs, the ones you mentioned, and the marginal revenue - marginal costs is large. But if your marginal profit is small, scale doesn't really help.

People like to compare Uber to Amazon and how long it took Amazon to become profitable. The differences are:

That Amazon was putting money into expansion and could turn a profit anytime it needed to.

AWS is their most profitable division - a category with high fixed costs and high marginal profit.

They are already using a lot of automation for their warehouses. It will be decades before driverless cars are ubiquitous.

In many markets, Uber will pay bonuses based on hitting a particular number of rides.