One reality that exists in every single game is that we have players of very different skill levels. More than land quality or anything else, it is certain that certain players will be on top in every game because they just flat out know how to play. Which is the genius of having everyone switch a few times a game. The good players would eventually find themselves leading the last place civs and those civs would benefit from their talent, whereas the dominant civs would find themselves led by the less skilled. This would provide some balancing in the globe, plus give people a more diverse set of experiences. Personally I love taking over a last place civ and rebuilding it. I imagine players who are used to always being in last place would love to take over for a leading civ like Russia or Neandor if given the opportunity.
It would really shake things up! Sadly, I couldn't keep it going past the first few turns.