I am most familiar with the thru-hike community as an example of 'extreme travel' and your observation that the urge to undertake a long and physically arduous trip often originates with a problem that the traveler hopes to solve does apply to some thru-hikers. I don't think it applies to all or even a majority, but it certainly exists.

The very fact of a long period of travel tends to place a break in one's life, where one's life story acquires a new framework of Before, During and After the Trip. The more extreme the trip, the more this is true. A big event like a thru-hike becomes a prominent landmark, like a marriage, birth or death.

Not everyone who is seeking this kind of Big Life Event does so from the same motive, but the motives do seem to cluster around several common themes. One of those themes would be a desire for more adventure and challenge, a feeling that one is not using one's potential or doing enough with one's life. Another theme might be a need to escape from life's many complications by reducing daily life to the absolute basics (I think this includes a lot of backpackers, but we're usually satisfied with a much briefer hike). Another would be seeking to fulfill the fantasy of oneself as a hero who requires a bigger stage upon which to play this role. Another would be an avid curiosity about new places, people and ways to be alive.

The motive of walking away from one's problems certainly fits into the list, too, but it's just one item on that list. I'm sure there are more of them than I came up with here.