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Everyone in this thread is wrong.
The answer is in 3 parts. First, we address rigid body collisions. Next, we address the physics behind this particular solution. Finally, we address the economics behind this.
First, Rigid Body Collisions: When cars were first being mass manufactured, alloys with a higher carbon fraction were used. This resulted in car bodies that were very rigid, and wouldn't deform upon impact, as well as other benefits, like lower cost of manufacture and (some) resistivity to corrosion. However, this meant that when a crash did happen, the body of the car would absorb very little force, causing the passengers to suffer a very rapid deceleration. As such, they were deemed unsafe. Today, cars are designed with "Crumple Zones", areas of the car meant to deform and absorb force, making it safer for passengers in the event of a crash.
Second, Physics: The operating principal of the video is Lenz's Law. An important point about Lenz's Law is that the force still exists. That is to say, the force required to stop the magnet still is provided by the chunk of copper, but the difference is it is an electromagnetic force, not a mechanical force.
Finally, Economics: Simply put, it's massively impractical. Permanent magnets are expensive and heavy, and electromagnets, while they have the advantage of altering field strength depending on sensor input, generally won't provide enough force without the use of supercapacitors, which run into economics issues of their own. Copper isn't the only material that could be used, but in general we would need a very good conductor. With that in mind, the main issues still lie on the magnets.
Now, tying this all together: In ths proposal, we run into the classic engineering bottleneck: Scalability. Using alloys and designs that crumple can be tested more rigorously, have fewer issues of scale, and requires no knowledge of the body being crashed into.
Hence proved bitches.
