Discussion of third-tier monsters.

Haven only has Djinns that can fly (though they mostly summon them).
Necropolis has Imps, Ghosts, Vampires, and Devils (or Bone Dragons).
Castle only has Angels.
Sylvan has Fairies, Griffins, and Phoenixes (or Magic Dragons, but they mostly summon them), and Mantises (or Air Elementals).
Fortress has Harpies and Storm Birds.
Dungeon has Ifrits and Black Dragons.

Therefore, Monks are good against Castle and/or Haven. With Fortress and Dungeon, you can use both Monks and Crusaders. Against Sylvan and Necropolis, only Crusaders are effective.

Against Haven, only Crusaders are needed. You forgot about forgetfulness. Against Castle, Crusaders are also better. Who else will help take down Angels if not them?