Obviously this is true, and especially important at low speeds, but I wonder how much difference there is between 70 and 80 — I would have assumed they are both typically fatal
One of my favorite trivia is the scenario that a car going 50 mph sees an obstruction in front and slams on its brakes and stops just in time just tapping it. A car next to him going 70 mph sees the same object, has faster reflexes, and hits his brakes at the exact same spot of the road. He slams into the object at 50 mph.
Just the difference between 70 and 80 is the energy of going almost 40 mph.
That's when the issue is stopping distance.
The issue on highways is that you have, for example, two cars in the left lane going 55 MPH and a third approaches going 70 MPH. One of the slower cars sees this and moves over but only at the same time as the faster car is changing into the same lane to pass on the right, so now both lanes are blocked, the faster car hits one of them and they're both edged off the road into a stationary object at highway speeds.
Does it matter if they hit the stationary object with significantly more energy? Probably not; dead is dead.
Meanwhile a significant proportion of accidents happen not because you couldn't stop fast enough but because you couldn't stop at all. Another driver side swipes you and rams you off the road and you're now three feet from a head-on collision with a utility pole; if you can even get your foot to the brake before impact it's not going to save you. You're driving on an apparently clear road in winter and come across a patch of black ice; your brakes have no effect and you're hitting whatever's in front of you at full speed. It's night, you're tired and you only realize there is a completely dark disabled vehicle in one of the travel lanes when you smash into it.
In cases like this the difference between 30 MPH and 50 MPH can mean a lot, but the difference between 55 MPH and 80 MPH is basically just "you're still dead".
No, kinetic energy is only quadratic in the velocity, E = ½ mv².