To replicate that, though, Uber would also have to replicate some of the state apparatus around it, which they may or may not be able to do (or even want to do, ideologically). The London exam is effective in part because it's backed by law: it's illegal to drive a taxi if you haven't passed a licensing exam, and it's also illegal for someone who is properly licensed to lend out their credentials to a friend who'll pick up some people on their behalf, while the licensed driver takes the day off. And as you make the exam more rigorous, those counter-pressures increase, so if Uber had an actually rigorous knowledge exam, they would also have huge levels of cheating if there were no attempt at serious enforcement.

Uber could try to institute both a rigorous knowledge exam, and a high level of enforcement of the rule that only people who actually passed it may drive cars under Uber's name. But they would need some credible way of doing that, like roving undercover inspectors.