What does a bow shot sound like to a deer from 20-30 yards away? Ever hunted in palmettos? Ever done it when acorns are falling? In many instances that sound can be significantly louder than many bows. Compounded by the fact it could be 5-10' away from the deer. If a deer reacted, and when I say reacted, I mean "ducking the string" and bounding away, every time it heard a noise equivalent to a bow shot in the woods where I hunt, the deer would never stop jumping. Deer encounter sounds of that decibel level, and sharpness, every time a branch falls out of a tree. Trees creak and pop all the time.
Is it different on a cold crisp morning with no sound, sure. Has a deer ever reacted to the sound of a bow shot? Of course, especially the closer they are to you. But I've watch a bunch of shots/reactions before voicing this opinion. And I repeat it's an opinion.
You can also see a different reaction in a deer 5 yards away and 30 yards away often times too. At five yards, they're ducking immediately upon sound hitting their ears, but the arrow is already on target. At 30 yards, you'll see them come to alert(ears forward, looking in the direction of the sound), freezing, and then ducking and bounding. If they were reacting to the shot sound only, they'd waste no time freezing to identify the sound.
Not really the thread to get this deep into the point.
I'm just pointing out that there's tradeoffs to everything. A faster arrow will encounter more resistance when it impacts it's target. And a loud arrow in flight is, at the very least equal to, but more likely in my estimation, worse than a quiet one when it comes to the reaction of the deer. Fast arrows get louder.