This is kind of an interesting concept...........
If you have a hot reliever who is not your closer and can pitch two innings consistently (as in Mariano Rivera in 1995), why not start the game with that pitcher? If you could get two solid innings out of a reliever at the start of the game, your actual starter would only need to pitch seven innings to finish the game. Or, that actual starter could pitch just six innings and hand it over to the closer for the ninth.
I would suggest calling the new relief position “The Opener.”
A New Kind of Starting Pitcher?