So are you suggesting that the interviewee goes through something similar to a portfolio? These are some of the projects I have done in the past, I wrote this code here to solve this problem, etc. I agree with something along the lines of "the best predictor of future performance is past behavior," but it could be hard to keep a consistent--dare I say level--playing field that way.
I completely understand where you're coming from, but I'm not sure that a level playing field is necessarily a good thing. Everyone should be given the opportunity to shine at their highest potential and it is my opinion that a level playing field gives candidates the opportunity to shine at their lowest potential.