Alice’s convictions, his belief in Iruma’s future, was that the reason why Amu decided to go along with his request? Or was it as simple as it being a rare personal request from him? Either way it’s certain that Iruma has some guards he can trust to take care of him, guards even Opera respects.
But… Iruma’s the only human here in Hell, and his enemies are the most vile of demons. If they really want him, there is no telling what they might do, or just how badly they might hurt both of the Asmodeuses. We don’t have a good scaling for Amu, but Alice has a limit we’ve been shown. He’s certainly very strong, but these enemies are far stronger, and far more cunning than those he’s faced in the past. And unlike those in the past, he’s going to be facing these ones head on, he has a target on his back now, at least for this event.
Seeing the danger he’s in, it wouldn’t surprise me if Amu somehow takes a hit in Alice’s place should things get messy. Though that’s just a hunch on my part.