Do we need to run background checks on the guy who puts cheese on your taco at Taco Bell? Or on a window-washer? Probably not.
Do we need to run a background check on the guy who may be driving around an intoxicated woman at 3 am in the morning? Yes, yes, and a million times, yes.
Maybe also check to make sure that he doesn't have a few DUIs to his name. Or, you know, a pattern of riders complaining about their driver being buzzed. They aren't even sticking to their own policy, there.
https://www.thefix.com/uber-faces-11-million-fine-over-drunk...
It's not like Uber is a rape fest touring the world in beat up lemons. In fact, I never even had an impolite conversation with the driver. It's just enforced with a different mechanism than background checks and inspections.
Frankly, I find the American paranoia behind running background checks on everyone much more bizarre than taking a ride in a stranger's car. And I highly doubt their effectiveness in a world where Reality Winner holds a (much harder to come by) security clearance.