One of the deer encounters led to an accident (worse for the deer), another one not listed also led to an accident (Volvo skidding down a slope hit traffic divider which got launched through the top of my car, instant convertible).

Human reflexes are actually quite good when you are in your twenties or so. The good news about self driving cars is that there will be less variance in reaction speed, as well as communications capabilities warning cars behind of obstacles and danger. Right now all we have to go on in this respect is brakelights but I think it is very well possible that at some point cars will purposefully communicate in some open format (broadcast) with other vehicles on the road.

Humans all having similar reflexes can be advantageous in a line of braking cars. Following a vehicle that can stop much faster than you requires a larger following distance.