Why not universal MMR?
Seriously though, why don't they use mmr? Wouldn't it be easier for Riot to keep track of one single mmr for one single account, instead of all these different mmrs for different game modes? Wouldn't it make the game itself far more balanced since you wouldn't have to worry about that diamond player whose never done an ARAM or Twisted Treeline pubstomping bronzies or whatever in these games just because he hasn't played them before? Does Riot think that good players in one game mode would all of a sudden be garbage in a different game mode? The mechanics of the game never change, so whats the deal?
EDIT: To specify, your ranked mmr is what is being used universally, and your mmr is only affected by your ranked performance.
Edit 2: If unranked, the players mmr is determined by performance in normal 5v5. If this isn't technically possible, they are considered "average" and are given whatever mmr that may be.