> the issue is that this is modeled as a very sturdy wall anchored to the Earth.
That's not what you modeled in the comment you linked. Your math (incorrectly) attempts to describe a car colliding with another car of equal mass. But if you're considering a "very sturdy wall anchored to the earth", then you effectively have a car colliding with the earth.
Either one is fine with me, but pick one. It grinds my gears when you authoritatively call me "absolutely incorrect", "correct" me with an incorrect answer of your own, and then try to claim you were modeling something entirely different all along.
The link I posted, https://news.ycombinator.com/item?id=40628932, clearly showed the kinetic energy math for both a car hitting a stationary wall at speed 2X, and 2 cars hitting each other each with speed X. This is basic high school math of inelastic collisions.
As per your "stationary" objections, the issue is that this is modeled as a very sturdy wall anchored to the Earth. Yes, the Earth will "recoil" some, but for all intents and purposes it can be modelled as completely stationary because its mass is so much greater than the car.