As was pointed out before, the issue is the change in velocity. Someone in the Honda frame of reference sees the Honda as stopped and the Tesla approaching at 80 mph. Then the collision occurs and the cars don't stop in that reference frame, rather they both move in the negative direction at 40 mph (assuming equal masses). So the energy of the Honda when from zero to 1/2 M * 40^2 and the energy of the Tesla went from 1/2 M * 80^2 (2 M * 40^2) to 1/2 M 40^2 and the net change in energy was M * 40^2.

An important thing to keep in mind is that the frame of reference cannot be affected by the collision or you must apply more math to adjust for the change of the frame of reference. You used a frame of reference that was similar to the Honda's before the collision, but then continued unaffected by the collision. That's a reasonable way to do the math as you don't have to adjust for changes in the frame of reference as the collision occurs. I'm not sure I'd call that "in the Honda's frame of reference" because it parted from the Honda at the point of impact - it's more "in a frame of reference that matched the state of the Honda before the collision". Either way, the analysis you gave was consistent with that "similar, but not identical to the Honda" frame of reference and that frame of reference remained unchanged by the collision so the math is good.

Most people try to apply the frame of reference of a passenger that sees an approaching object at double the speed and then continue mentally anchoring the frame to that person through the collision to the aftermath and that leads them to think of a 40+40 head on collision as involving an 80mph change of velocity, but they cannot hold on to the frame of reference like that as they suffer the collision and get correct numbers.

Crashing into a parked car at 80 mph is very similar to two cars hitting each other head on going 40 mph.

Not really. All they have in common is some numbers that add up to 80, crumpling someone else's property, and the look of fear in the passengers eyes as they watch the "approaching" other object. But, their energy is quite different. In particular...

However, that's not the same as hitting a brick wall at 80 mph even though the energy is the same.

Hitting a brick wall at 80 is similar in terms of energy to hitting a parked car at 80, true, but neither has the same energy as two cars hitting head on at 40+40. For "80 into brick wall" and "80 into parked car (assuming the car is anchored well enough not to move)" have 1/2m80^2 or 3200m energy. The head on 40+40 cars have 2 * 1/2m40^2 or 2 * 800m or 1600m or half the energy of the single car 80 example.

The difference is there's no crumple zone in a brick wall so the average deceleration of the car during the crash into the brick wall is significantly higher.

Hitting a parked car does add more crumple zone than hitting a brick wall and that helps, but two cars hitting each other at half the single-car speed not only have the extra crumple zone, but they also have half the energy to deal with.

The other consideration is that hitting a parked car at 80 will probably result in a deceleration of <80 because you are going to carry the parked car along unless it had a bat tether wrapped around a very large utility pole.

So, hitting brick wall at high speed gives you 1 crumple zone and high energy.

And hitting parked car at high speed gives you 2 crumple zones and high energy (and probably residual velocity that lowered the total energy of the collision itself).

But, hitting another car with each of you at half that speed gives you 2 crumple zones and half the energy of either of those two.

And that is assuming that the two cars are of similar mass and end up stopped at the point of impact.