At the risk of being a contrarian, even that scenario of driving into a national park until you can't drive and then walking is probably a guarantee of you being found. National parks are managed land and they're pretty popular. You're also leaving your car behind, either on a designated access road or a fire lane which makes finding you more of an inevitability than anything else.

Part of what I do for work are wildlife surveys. People tend to steal the cameras or the SD cards. Something I've noticed is that when I look for places to put cameras, specifically to avoid capturing humans, I still get humans on them, or the cameras are sometimes tampered with. I think this is a sort of confirmation bias. Anywhere you or I go, someone else is likely to go. Even if we're trying to hide, we still have shared common biases.

The least likely places for humans to go are the ones selected at random via GIS on a map. I select 10 random points in the management unit then i rule out the obvious bad ones that intersect with an access road or some kind of facility. The trouble with these points is that they tend to be really hard to access.

But you know what? I do think this is kind of splitting hairs. Obviously there are always remote areas, and a determined person could hike for many hundreds of miles.

I think the bigger factor in "disappearing", whether it's for some nefarious reason such as suicide or not, is how well known you are. Are there people who are motivated to find you? Are the local police well funded? Are there land management staff here willing to look for you? How many years will your spouse, parent, child look for closure? I think for most affluent people, enough of these factors align to make them easy to find. Those most capable of disappearing are those who have nobody. Unprivileged people, who don't have the support structure that they need. This sort of person can disappear even in a well populated area. Where I live, there are many road signs warning of human trafficking. I suppose human trafficking is probably the leading cause of true disappearance, since the victims often fall into that category of person who has nobody.