I think it would be great if we had a "legal directive in case of disappearance" similar to a will, power of attorney, Do Not Resuscitate (DNR), organ donor directions, etc., that names people who have the right to act on your behalf if you disappear.
I'm really actually surprised this isn't done as a routine along with all those other things. If I go missing, I want my family to be able to access bank accounts, cell phone records, etc. You could just name one or two people, the way you name powers of attorney, and at such time they believe you are missing (you wouldn't even have to put a time frame on it, no number of hours, just the person's best judgement) they can access your records to attempt to find you or determine what happened.
Of course, you would have to have certain parameters - attempted cell phone contact, attempted contact at work and home, and close friends, etc.
If you don't want people to look for you if you disappear, same as if you don't want to donate your organs upon your death, just don't sign one.