One interesting question which the Royals will need to address is what to do with Butler or Hosmer in away interleague games. Only one will be able to play 1B with no DH allowed. Also, the decision will need to happen rather quickly with the second series of the season being at the Philadelphia Phillies April 5th to 7th.
This season, with the Astros moving to the American league, there are 15 teams in both the A.L. And N.L. An interleague series will be in process throughout the entire season. Interleague play will not be grouped into a couple of blocks of games like in past seasons. Instead, it will be all spread out. Here are the 4 series's the Royals have to play without a DH:
Apr 5-7 vs Phillies
Apr 16-17 vs Braves
May 29-31 vs Cardinals
Aug 2-4 vs Mets
For the Royals, a problem arises when one of the team's top 5 hitters will have to ride the pine for nine because there is no DH. Either Eric Hosmer or Billy Butler will be on the bench. Butler is probably the team's best hitter (I know it can be debated Gordon is the best) and Hosmer is not far behind. Neither of the pair really has another position they can play. Hosmer tried RF last season and here is a video of how it went.
I think Butler should be given the opportunity to start each game since he has shown he can hit in every season he has played. What I think will happen is Yost will go with the hot bat out of Spring training. If they are both hitting the same, a platoon may happen with Hosmer facing right-handed pitchers and Butler facing left handed pitchers. No matter what happens, it will suck to have one of the better bats sitting on the bench.