Kinetic energy is totally dependent on speed.
Kinetic energy is dependent on both velocity and mass, not just velocity.
The reason kinetic energy was popularized was the advent of high velocity small caliber cartridges and the publicity surrounding them.
Whether or not that is why it was popularized, it came into use in the first place, and has stayed in common use because it is a scientific quantity which quantifies the
potential of a projectile to do work/cause damage. There are any number of reasons why a projectile may not do as much damage as it has the potential to do, but kinetic energy provides a good starting point for those who want to try to boil things down to a single number.
For what it's worth, I don't believe any single number comes close to telling the whole story when it comes to insight into terminal effect, but if you're going to pick only one number, you could certainly do worse than kinetic energy. Momentum is another scientific quantity which provides insight and which is used (though not as commonly) to attempt to quantify terminal effect, especially in handguns.
Dr. Martin Fackler proved long ago that only the permanent wound channel mattered in the lethality of any hit.
While he did make the claim that temporary cavity was not a significant wounding effect, it was specifically in reference to
handgun caliber lethality, not rifle caliber lethality. While that is generally accepted to be a fairly accurate generalization, it is not a universal truth, nor has it ever been conclusively been proven to be universally true even when applied only to handgun caliber lethality.
In fact, temporary cavity can have a significant effect on lethality even in handgun calibers--though it is generally not very reliable even in the more powerful handgun calibers.
Here's a quote from Dr. Fackler. "It should be noted, however, that stretch from temporary cavity tissue displacement can disrupt blood vessels or break bones at some distance from the projectile path, just as they can be disrupted by blunt trauma."