I must be totally dense because I am not understanding this at all. As an example, the security system in my home has a duress code that I can enter which disarms the alarm while silently alerting the authorities that my duress code has been entered. In most cases, this is probably sufficient. However, for certain adversaries who are aware that a duress code exists, they could make the "bargain" with me that if I enter a duress code, they will murder the rest of my family. They might not know that my duress code has been entered, but if the authorities come poking around, they will know.

So, in Alice's case, she gets kidnapped. The attackers are aware that she might have a duress code. They tell her that if she enters the duress code, her entire family will be murdered. If Alice lives in an area where authorities are in bed with and inseparable from the criminal element, is she going to take the risk that the authorities are alerted?

If we are talking about a panic code which erases all information on the phone, do you not think that the same bargain can be applied? In fact, such a system might get innocent people murdered and needlessly tortured since, if someone is suspected of having sensitive information - but actually don't - the attacker might get the idea that a duress or panic code was entered which deleted said information.

In any case, it doesn't seem like encryption is going to save people from real harm.