You are correct - if the "stop" is at a constant deccel rate, whether by braking on a runway or sliding across a field, the distance is proportional to the square of the speed.  However, if it is more of a constant-distance thing the "severity" is roughly proportional to the cube of the speed.  Problem is, you don't don't know which condition is governing until you get there.  Even if you are sliding across a field at twice the touchdown speed (I use the word "touch" loosely) you have four times as many rocks that you could hit and each rock could do that much more damage at the higher speed.  Thinking of the potential damage as a function of the speed cubed tends to add emphasis to the approach speed control.  If your plane stalls at 60kts, impacting the ground at 75, still below a normal approach speed, can potentially double the severity compared to impacting at the lowest possible speed.