One thing which I think could hold projects like this back a little is the cryptocurrency component. I haven't delved into developing with Ethereum yet... would it be possible to use the non-cryptocurrency components with a FIAT payment system such as Stripe or Paypal?

Sure. Think of Ethereum as a global computer that coordinates human interactions. On top of it, you encode the rules that those interactions should follow, and a mechanism for recording who has been following the rules and who hasn't.

A decentralized Uber would have logic that records how often drivers show up when they offer a ride, how often they're late, how clean their cars are, etc. It would have similar logic for riders to handle their end of the interaction like the one you pointed out: did they pay what was agreed on?

The payment mechanism is irrelevant. Driver and rider satisfaction is what matters, and that's easy to track without putting any limits on their real world interactions.

Banks don't normally give bank accounts to robots.

They do and very frequently. A big chunk of intraday trading of currencies and bonds is done by bots that connect through APIs to brokers like interactive brokers.

There a some mutual fund companies that have "black box" investment managers, which are computer programs that manage whole portfolios and trade their institutional accounts at investment banks.

Program trading on the NYSE has been active since the 1980s.

They gave the account to a company and the company delegated access to a robot. However the account is not in the name of the robot.

They do to companies though.