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.

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

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.