The only reason Arthur did not rush in attacking everybody was because he was not sure if Elena was safe. One strange noise could make these bandits go all out and kill her.
It would be a disaster! He was not there to punish bad guys or anything like that. Arthur was there to rescue Elena, so he should focus on that, and not on attacking bandits like a madman.
But now everything was different. He had the youth who hired these bandits right in front of him, as well as the leader of those bandits and Elena itself.
"How should I go about this? Killing everyone and flee with her? No, that could traumatize Elena and maybe my reputation can be tarnished on my first day here."
Arthur thought about how he should proceed with the situation, and he opted to just use his identity! Elena was going to the One Hundred Thunder Academy, and he had a tremendous authority there.