given the stated reaction time, of a white tail deer at .08 seconds,
lets say its reaction time to a shot is from a rifle throwing a projectile at 2700-to- 2500 fps,
average white tail deer are shot at well under 150 yards
(Id bet the true average is well under 80 yards,)
and at any range over 150 yards, I doubt the deer would pick up the muzzle flash,
and certainly could not hear the shot before bullet impact.
simple math, if we were to even assume even a slower, 2300 fps x .08 seconds reaction time,
the projectile has already covered at least 184 feet (61 yards) of the distance to the impact point,
before the deer could, even begin to react or move any significant distance,
boost the velocity to 3000 fps and your closer to 80 yards the projectile has traveled before the deer could begin to react,
so while its might be potentially possible under ideal conditions for the deer,
I doubt its a significant factor in most people missing.
ever year we have a impromptu rifle accuracy contest the target is a 3" diam orange dot,
the contest involves each participant walking briskly back from the 100 yard target backer,too the range, safe shooting line,
immediately dropping to a seated position with his deer rifle and firing at least two but hes allowed as many shots as he can fire in 10 seconds
only the closest two bullet impact point,s to the center of the target count, in your score,
obviously smallest total distance counts, and you would be astounded at the number of people,
that can consistently shoot 1" bench rest groups that can,t consistently punch holes in a 3" orange dot without a bench rest.
Id strongly suggest most misses are the result of lack of hunter competency with the chosen weapon,

years ago I saw a game department survey made where they asked hundreds of hunters at a western BLM check point, to look out at 5 different colored flags placed at random but carefully measured distances and write down what each person estimated the distance too be from the check point, they were handed a pen and a survey card, they were told NONE of the colored flags were at an even 100 yard multiple but that was the only info , each flag was a different, color, placed in a
different direction and at a different distance.
the survey taker pointed out each colored flag and asked them to write down their estimated range!
they tabulated the actual hunters field estimates being made on the spot, vs the carefully measure actual distances.
.
.
the results were about what Id have expected..after decades of listening to guys claim they killed deer & elk at 400 and 500 and 600 yards.......
the vast majority were very VERY bad at estimating distances correctly past about 150 yards, some estimates that were over 70% wrong were not uncommon

yes thats a mule deer, but even mule deer are rather commonly shot at under 150 yards
use some rifle like a 25/06 with a 120 grain bullet, a 270 win with a 130-140 grain, or a 30/06 with a 150 grain, thats pushing bullets near 3000 fps,
and you can be rather sure that deer reaction time,is never a significant factor in you missing a deer.