So like an 'anything goes' variant? That's not chess! Hmm seriously though, I'm not sure how popular it would be. I guess we'll know based on the feedback the thread gets.
What it does make me think of though, as a random throwaway idea, is if there was an option to input a PGN into an unrated game and choose a starting point. So, for instance, if you wanted to play out the endgame your own way of one of the games of your favorite world championship match, unrated, for instructional/learning purposes or for fun. Or start from one of the middlegames of Alekhine's games and see what tactics you end up finding, then later comparing it to the book game.
This would then allow you to create PGNs with really crazy positions if you wanted to go through the trouble.
I don't know if this is possible or not but I was thinking about how cool it would be to have the ability to make any starting position to start individual games or a tournament.
For example, consider a chess game where everything is the same except that one side has all pawns turned to knights while the other has all pawns turned to bishops.
Such games could be either unrated or have a separate rating kind of like chess960 has a different rating.