why couldn't she just wait for them to come outside?

There's no guarantee the King would step outside the Palace, and the entire Palm infiltration was one of the contingency plans to try and get more information before the Invasion.

The entire mission was basically a suicide mission anyway so Palm was willing to risk her life on the off chance they can get information, and in any case Knov planted exits so Palm could back out anytime (before she was caught). She just got extremely lucky with the Pitou/Pouf En switch that let her get somewhat close in the first place, but then got extremely unlucky when the En turned back on and she was caught.