Traffic fatalities were 37,757 in 2015, and 40,200 in 2016. Self driving cars aren't going to do worse.
The question isn't whether they'd do worse. The question is whether the increased cost of the automated cars is going to improve these numbers sufficiently to make the technology viable from a purely financial standpoint.
I can tell you that there are some measures you can impose that would be a heck of a lot more cost-effective in reducing motor vehicle fatalities than "self-driving cars." I'll list three of them right here (and the third one sounds ridiculous on its face but would eliminate most of the problems with distracted drivers):
1. Seatbelt activation devices that automatically reduce speeds and/or disable the ignition system of the vehicle unless the seatbelts are used.
2. Speed restrictors on cars (limiting the maximum speed of every vehicle to 60 mph will reduce fatalities considerably; limiting it to a ludicrous 25 mph to eliminate in-vehicle fatalities almost entirely).
3. Outlaw the automatic transmission.