This all sounds like the Soviet Union. "Your papers must be in order!"
I don't really see it as any different than being obligated to file your taxes every year or file custody paperwork when divorcing, or having to take time off work to perform jury duty, etc. As adults, we have obligations and responsibilities, whether it's fun or not. I'm not saying that people shouldn't be able to take off if they choose to. But to waste government and media resources as well as time and money for search purposes, when you don't want to be found, I DO think that should be a crime. I'm not suggesting some long drawn out process where you have to legally "divorce" the people in your life, or anything crazy. I'm talking about a legal form, that can be filled out in front of a legal witness and notarized, for a reasonable sum, and then entered into a database. Basically, a formal legal declaration of an individuals right and choice to leave their current life behind.
If a mother and father divorce, and the mother has custody, she can not legally (at least in most states and in typical circumstances) move out of state without the father's approval. Wouldn't that also be very "soviet union" by your same standards? It seems unfair and improbable that a mother could be FORCED to live in a specific state because the father of her children refuses to agree. But at the same time, it's not necessarily fair that the father has to live states away from his child just because he's not married to the mother anymore. I bring up this example only because I feel that the issue of people choosing to disappear is not black and white. There is no PERFECT way to deal with it. But I do feel that it would be more appropriate for the person who chose to disappear to deal with the consequences, than for the community, LE and other missing persons cases to suffer the consequences.