they get real flappy

Metal does not like to compress at all. But when you make it really thin it will be floppy like a spring you might find in a pen or wind up toy. However you can make it stiff again by making it curved so the sheet has structure/mass going on all directions. Infact believe it or not cars during the 1960/70s had quite a bit of curves dispute being a brick. And that's because they didn't want the panels to dent easily. So when a car has flat faces like the Cyber truck. Those panels don't even have subtle curves to give them structure and they are soo suspectable to dents that a simple brease does the job of denting them.

I assume the flat panels have an aerodynamic effect like the underbody of race cars. They ultimately create forces sucking the surface into a direction. And since on the sides it will be never stable it will flap around all the time. You can see that the most with the vertical fin stabilizer of Formula 1 cars. https://old.reddit.com/r/F1Technical/comments/nd2ayw/alpine_flexible_rearwing/

Here is a lot of wobbling and while the vertical changes are intended, the horizontal ones surely aren't and they tried to make it as stiff as possible. Certainly nothing a production car would achieve.

Correct me if I am wrong, as I didn't study this particular area.