The article makes no mention of services like Uber, or the myriad new delivery services popping up. Surely those must increase traffic and thus an increased risk of accidents, fatal or otherwise?

It'll probably take 10-20 years to have fully autonomous cars but with deaths increasing, the case can be made to provide more assistance from the computer driver.

I think it's actually unclear whether fully autonomous or driver assist will be the technology that wins in the end. There are points for both, and one may not actually lead to the other in a useful manner (people may be unwilling to make that small jump to fully autonomous where they would if forced to. There's actually historical precedence for the situation we see ourselves in now, elevators went through a similar technological change.

The 99% invisible podcast[1] actually went pretty deep into this in episodes 170 and 171, and they were excellent shows.

1: http://99percentinvisible.org/