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.

Where I live, Uber solved the getting home drunk problem.
Public transport isn't open at night.

Of course Uber wouldn't help traffic.

Robotaxis? Probably not. But autonomous vehicles that can communicate and drive as a group? Yes that will help. Then induced demand and all that, but it will increase capacity.

Everything that encourages someone to get in a car will make traffic worse.