I had a similar idea, but it was more about changing places very swiftly, the rules of the show wouldn't allow staying in the same place for longer than a day/three days/a week, depending on how big of a location we're talking about. This wouldn't be about making a life for yourself in a certain place and then ditching it, it would simply be about traveling fast.
The rules of such a show could be set in a few different ways. One way is not to allow sleeping in the same place for longer than one night. By sleeping/staying a second day in the same place you already get the feeling of familiarity and usually a certain degree of boredom with it too. To keep things fresh, you have to move constantly. The limitation of this is that you can simply stay in the same city/area and just rent different accommodations every day which might become boring for the viewers fast.
Another and maybe better set of rules would be to not allow the participants to stay in the same country for longer than..... this part is quite difficult to decide upon, a day is too short, cause you might not even manage to get out of certain countries that fast, not to talk about getting a decent amount of sleep. Three days might be a good amount of time, you come and settle on the first day, do some sightseeing on the second, and get out on the third and the cycle starts again. If this is still too short then a week should do. The final aim could be to visit all the countries in the world and it would be done in a record-short amount of time.
The rules can also be more complicated than that, different aspects could be combined - you couldn't sleep in the same place for longer than a day, couldn't stay in the same city/area for longer than x amount of time, and couldn't stay in the same country for longer than y amount of time. This would be a bit of a mad race, but an interesting one, it would be a bit similar to this.