I recall discussion of cosmetic things like unique tower and wall graphics being experience rewards or things "purchased" with a currency earned through playing matches. I still think such an addition (without things actually affecting game play) would be fun.
As for attaching such a thing to starting attributes, I can't even begin to think about what it would be like to try to balance everything while taking these into account as well. My guess would be that the amount of necessary consideration would be multiplied by the number of different options.
If you did want to pursue this, however, I would ask that it be an optional game mode just as Hidden games are now.