As usual a purely physics based approach assumes a lot of variables. It takes me little thought to imagine many problems with this, I live in Oklahoma and this situation isn't rare. The described deceleration is assuming the cubic object is traveling on a friction-less surface that hits a static object at a known rate in an inelastic collision. So many more variables. Vehicle flips, vehicle spins and takes out the 2-3 vehicles behind it, vehicle is bumped into a guard rail or bridge support and has a very very rapid rate of change in velocity. Or a truck is jarred and the shotgun in the back seat shoots too many holes in your assumptions.
Yes, control systems can react much faster than humans; however, the statement "The car behind will apply maximum braking force the very moment a single cycle of it's control loop happens (probably 1/1000 or a second or so)." is almost patently absurd and shows a best a limited understanding of tuning a control loop. Yes, a reaction will happen within a single cycle, and yes 1kHz is reasonable, but assuming maximum braking force is assuming it is only a proportional control that is tuned to be highly reactive. I would challenge anyone to ride in a car that has a purely proportional control that would react as described. You'd sue me for whiplash.