"It basically shows you do not have a political affiliation to any one country."
No, it shows that someone is playing fantasy games and is too chickenshit to REALLY cut the ties.
If you really ant to show you have no political affiliation to a country, you formally renounce your citizenship, you cut that sovereign loose, and you apply to the UN as a "stateless person" for travel and identity papers. Yes, there are such things. Yes, they are recognized, and no, they are not fantasy passports.
But first, one has to have the courage of their convictions and renounce that citizenship that is so opressive and unwanted. I know someone who climbed a wall and renounced Russia
. Someone else who held a highly esteemed position, but chose to hike out of Czechoslovakia in the dead of winter too. Both would have been shot if they were caught.
Fantasy passports? Not quite the same thing.