Key point is that they have all relieved before, at some level. They do it all pre-season getting ready. We aren't reinventing the wheel here.
Sure they probably won't be the first choice for a mid-inning appearance in the playoffs but they can certainly start a fresh inning anywhere in the game. They will know who's on tap for a given day and be ready, just like the rest of the pen. It's still pitching, we aren't asking them to DH.