Actually, Lyft and Uber's model does help eliminate incompetent, scary, and dishonest drivers. All passengers are prompted to rate their drivers at the end of the ride on a 5 star scale. Any driver who drops below a 4.6 average will be offboarded from the platform. Can't speak for Uber, but with Lyft, if a passenger leaves feedback about the safety of a driver, that'll also get the driver suspended until the performance team can investigate the claim.
If your Taxi driver is unsafe, who do you report him to? How about if he rips you off? If there is anything that is wrong with the service, from car maintenance, driver hygiene, navigation, safety; the passengers are able to remove the driver from the system