It would kinda break the game. The whole point of not having each side completely the same is that it adds deeper diversity based on the side you are on. Right now if you are on the Radiant or Dire, it effects your draft / laning...etc. Even changing something like the perspective is a slippery slope where it begins to get away from being the same every game for everyone.
I would say just keep playing or play some bot games on the dire side and you wont notice it anymore. It seems like most newer players prefer Dire side anyways because they manage to click the minimap down in the bottom left when they are on the radiant side, which leads to a lot of useless deaths when they could have escaped.