Other teams would sit too long.
I think they would make the WC team earn it. Game 1 and 2 could be a double header. Season ends on a Wednesday, WC DH on Thursday, final WC on Friday, first NLDS games on Sat, then WC winning teams play Sunday. Don't really even need a DH, could make them play right out of the season 3 straight games. No rest, that's what you get when you don't win the division.