Letting Alicia do her thing was fine, but he should've had a plan for when it failed. And frankly, Alicia did fail; the dipshit Prince only backed down because Mariana was willing to risk summary execution to get through to him.
This is a society where duels are a thing. After all, that's how Patricia and the Prince got away with burning Alicia's face in the first place.
Ragna has more and better options than (1) stand there like a lump or (2) blindly lash out.
Ragna is a hammer that has the ability to turn his problems into nails. He's a complete schmuk if he isn't keeping that (and possibly other options, it really shouldn't be on the readers to figure out Ragna's options) on the table, especially when he knows he, his fiance, and their commoner friend are all being targeted by idiots, psychopaths, and idiot psychopaths.