I would think most people would spend money and time searching anyway, and it's pretty hard to travel far in our modern world without leaving a trail. Seems like they'd spend days or weeks worrying and searching, probably end up finding your body anyway, and what if they get a bill for the search effort?
And if they don't find you, that might even be worse. I've met people who are still wrapped up in grief and denial and trying to find a loved one *years* after they went "missing", and it's just horrible. They know, but they can't accept it on the desperate hope that their loved one is still alive, so they're stuck in a horrible grieving-but-not-grieving, knowing-but-hoping, putting their lives on hold in a futile crusade to bring back their loved one alive.
Once upon a time, I considered moving abroad, or spending a year traveling the world or the like, and winding up dead where I'd never be found, or just not noticed among the all the other bodies. I figured out that would just draw things out, though, keep them suffering indefinitely. Their going to worry and grieve, may as well let them get through it quick.
The presence of a body does generally help people grieve and move on, though it's best to arrange to have someone else find the body, so I think that's the way to do it, at least in general.
