That's a really good point that many (myself included) aren't mentioning. Stopping distance is a universal, reaction times be damned. Would be curious to see if that played a part.
Sometimes the best reaction in this situation is not to stop, but to swerve around the obstacle, perhaps even accelerating slightly to do so quickly. Deer can be pretty unpredictable here, but most on foot humans will not put themselves into the new path of your vehicle.
Perhaps (self driving) cars can be redesigned to mitigate the outcome of pedestrian collisions, eg, like cowcatchers on trains [1], except something more appropriate for the situation. External airbags?
