We already have a system for privatizing negative externalities in traffic accidents (and in 95% of the rest of life). It's called tort law, and it will certainly be used in this case if Uber was at fault.
There are of course situations were externalities fail to be privatized (e.g., traffic congestion), but I don't think auto accidents is one of them.
There are of course situations were externalities fail to be privatized (e.g., traffic congestion), but I don't think auto accidents is one of them.