I don't buy the Kinetic energy whole-heartedly, but I don't disgard it either.
Energy dumping is definitely what a bullet does. And how violently it does that determines how much tissue damage is done.
Like the saying goes, "it isn't the fall, it's the sudden stop at the end that kills you." (in reference to falling from great heights). It is much the same with bullets. It isn't how fast the bullet is going, it's how much it slows down.
To measure energy transfer you would have to set up a chronograph right before the deer's chest, and one immediately on the other side. You measure the spead of the bullet going in, and the speed going out. If the bullet fragments, you would also have to weigh the bullet before and after. With those numbers you calculate the Kinetic energy the bullet has at impact, and the amount it has left over after exiting, the difference is the amount transferred.
To say that a bullet that stops on the other side is the ideal is stupid. That just means that the bullet dumped all it's energy in the animal - it doesn't mean that it dumped a whole lot of energy.
For example, I can shoot a whitetail with a .54 caliber roundball at 100 yards and recover said ball from hide. I can kill similar deer with .30-30 at same distance and have an exit wound.
At 100 yards my .54 ball will have roughly 650 ft-lbs of KE by the time it impacts the chest. Since it didn't exit, I know it dumped 650 ft-lbs of KE in the deer.
At 100 yards a 150 grain .30-30 bullet will be going 2018fps, carrying 1356 ft-lbs of KE. If I managed to get the deer to stand between chronographs, and I clocked the bullet exiting the chest, say I got 1,036fps as the exit velocity. And to make the math simple the bullet retained 100% weight. So before impact the KE is 1356ft-lbs; after impact the KE is 356ft-lbs. The difference is 1,000ft-lbs. That means 1000 ft-lbs of KE was transferred.
Even though the .30-30 exited with over 3/4 of it's impact velocity, it still dumped more KE than the .54 roundball did. Mainly because the .30-30 had more KE to begin with.
So exit wounds mean little, in terms of how much net KE is dumped.
Energy transfer has some, limited meaning when we try to predict the size of a wound channel. For example, take a 150 grain .308 win soft point vs. a full-metal jacket military round. Same bullet weight, same velocity, same KE at impact. Because the fmj retains its aerodynamic shape it will whistle on through a chest cavity and it's exit velocity will be much higher than the soft-pointed bullet. So one will transfer more KE than the other. Guess which one will have a bigger wound channel? The one that dumps more KE. And it's not simply due to the bigger diameter of the mushroom - how else can a .75" mushroomed bullet creat a 3" wound channel?
Finally, there are often two different criteria for hunting bullet discussions. There is the "Drop-in-its-tracks" criteria, and there is the "Clean, humane Kill" criteria. Dropping-in-its-tracks is a subset of the Clean, humane kill. You don't need to drop a deer in its tracks to cleanly and humanely kill it. This is so important I'll re-type it. You don't need to drop a deer in its tracks to cleanly and humanely kill it.
Obviously, dropping a deer in it's tracks is dramatic, convenient, humane, and fun. So people have set out to determine how much hit it takes to consistantly get this performance. Unfortunately some idjit came along and applied that criteria as the minimum necessary for a humane kill!!!!!
Now a .357 bullet may not consistantly drop every deer in it's tracks, but if they fall within 100 yards or so - the .357 certainly made a clean, humane kill. I don't know how long it takes a deer to cover 100 yards, but highschool track athletes can cover it in less than 10 seconds. That means even though the deer covered a long distance, it's pain and suffering lasted less than 10 seconds, probably WAY less. That's humane.
The real reason for speed:
The main reason ammo companies are going gonzo for velocity is to get .30-30 performance at longer distances. Look at the KE figures for .30-30s at 100 yards, then compare to a .300 Win Mag at 400 or 500 yards - yep, about the same. So the 3000fps isn't to really hammer deer hard at 50 yards, it's to hit 'em like a .30-30 at 500 yards.