All these things are near impossible to an average human driver, but there's no reason why an AI would have more trouble looking behind than forward.
* If there are enough self-driving cars, it will also (hopefully) teach those drivers who feel entitled to go 90mph at 3am that tailgating is no longer a working strategy.
Any sufficiently advanced self-driving AI will try to avoid being rear-ended like that. Even better, when a collision is unavoidable, an AI has a much better chance at making the 'right' decision as to how to crash.
"The central zones of $CITY are self-driving only". You could still use your normal car to get to parking lot near the city and switch to public transport but if you want to get INSIDE the zone then you need to be self-driving.
(On sidenote, you could have self-driving electric taxis that ONLY serve inside the zone as well as zone-only buses)
Then gradually expand the zone.