Except that you'd be:
A) Taking a reliever out of his comfort zone.
Your whole premise is wrong, because after probably the first two guys in the 'pen, all of the other relievers are essentially guaranteed to have worse stuff than your worst starter even in an elite bullpen.
c) In an elimination game, with all hands on deck, you can pitch your starters who have the most rest, and are obviously better than the mid-bottom rung relievers of your roster.
D) You essentially force your specialists into one-inning situations.
E) It's just a terrible idea, because what happens if by miracle you don't get shitstomped and the game goes to extras, and then you have to warm up a .starter on short notice instead of piggybacking starters, which is the logical choice?
Straws are not good to grab on to.