Regardless of anything else, there are no circumstances under which companies like Uber would decrease traffic. This is because of two effects: Firstly, any regular car ride replaced with an Uber ride will result in more road-hours, since there is now a car travelling to your pickup point as well travelling on the road after dropping you off.
Secondly, the convenience of Uber can cause more travellers taking a car instead of public transport, again increasing the total number of road-hours.
Is there even a hypothetical scenario under which any of these private hire companies would reduce traffic? The only theoretical benefit is that less parking spaces are needed.