Even the gameday part is not true at least not really. It's like saying a t-shirt will protect you from a gunshot.

Yes they do in theory provide some support but the support they give is so little that it would literally never prevent an injury. The ammount of force needed to injure your ankle is so far beyond what a little bit of fabric or leather can protect you from that it's not even worth mentioning as actual protection.

This shit needs to die. High tops do not protect ankles at all. It's a complete myth