It's not really paper thin btw.
And what has to be dissapated isn't kinetic energy, it's momentum. if I fling you at 60mph into a brick wall, your kinetic energy is dissapated completely, but the change in momentum (impulse, or force integrated over time) is what kills you. You can reduce the blunt trauma in two ways, spreading it out (lower pressure) or spreading it out in time by absorbing the momentum over a distance. Ballistic vests use both, though your body provides the distance for the latter. Theoretically, an infinitely stiff, material would reduce the pressure the most, but then the energy would be deposited into the material locally, and melt it. It's a trade off. These materials show promise for some applications, mainly hard armor. For soft armor, shear thickening fluid impregnated cloths show significant promise as they can supply both stiffness and elasticity as required.