There is too much of a skill difference inside Silver. So much so that many Silver players keep getting fucked over by fresh lvl 30's who get placed in high silver by winning 4 games in their placements (some deserve to be there, and some definitely do not.).
Because of this, there is a wide range of skill in Silver alone. I'm Silver 2 right now, and every single one of my games goes one of two ways:
1. Annihilate the enemy team into oblivion
2. Get annihilated into oblivion by the enemy team
There is no in-between.
I don't know what this division would be called, but it would definitely divide the players into the proper categories of skill and make the playstyle more effective to a player's skillset.
I mean, Riot added Master division to keep Challenger fair enough. It shouldn't be too hard to add another.