Nothing. It was just an assumption made for the sake of simplicity. Since the crash is assumed to be inelastic, it makes the math much simpler. In the real world, the impact would NOT be completely inelastic, and in fact some of the energy would be transferred into movement, by both cars. We can't really get into impulse force dynamics without knowing the relative elasticity of the cars. So exactly how hard do we want to make this? We also need to know exactly how long it takes both cars to transfer this momentum, since Joules=kg·m²/s². We simply don't have enough information to take all this into account.