I believe I answered this in the other thread too, but the character's hesitations are for storytelling purposes. The player who views the story needs to have time to emotionally react to what is happening and process new information. Most of the hesitation on the player's character is to allow this to happen. They aren't a perfect reflection of what would happen in real life, but suspension of disbelief is important factor here. You have to let the game dictate rules of reality when in the story, not real life or you'll always feel that something is off.

So what your refer to as lazy writing, is your refusal to except suspension of disbelief. You have also forgotten that the player character wants to save Mikoto more than just trounce Misija (Mikoto's safety comes first, so you hesitate to save her life and have to react to the full scale of Misija's betrayal). You have also forgotten the Misija gets shot after kicking Mikoto away and being distracted tempering the Blades while the player character acts appropriately shielding the remaining soldiers. In universe this all makes sense.

All seriousness aside, WHM couldn't rescue Mikoto because they weren't in the same party.