They will make it worse, as it makes it easier to move a vehicle around. When the price goes down, the usage goes up. And it's traffic whether the vehicle has a human being transported, it's circling waiting for a fare, or it's on the way back, empty, from taking a child to school
You no longer need inner city parking, and people will be more willing to jump on public transport to skip traffic because you are not bound by the location of your own car anyway.
you are right, it probably won't fix the traffic, but it doesn't matter because if you are not steering the wheel then you can work or study while in the traffic.
They might fix it a bit. Cars might be able to travel at more consistent speeds, not speeding up and slowing down, that causes traffic, and fewer accidents would also reduce traffic.
Maybe in the future they could also travel closer together!