The padded hats I referred to are very effective at reducing the deceleration force of low-force impacts. It's these low-force events that people complain about the most, like the trunk lid incident.

Padded hats are not effective in high-force impacts, such as a bicycle crash, because as you say, they don't reduce the deceleration significantly enough. That's why they are not meant to replace bicycle helmets for cycling.

These hats will also reduce anxiety because they give you a sense of security so you don't have to worry about hitting your head. And if you do hit your head, it will be a significantly lower impact so your brain won't over-react with excessive anxiety or inflammation.