Revealing mistake: When Benji imagines putting on a mask of an agent he plans to impersonate, when the camera pans around to first show the mirror, the mirror Benji's hands are further up on his face than the reflection, and the mirror Benji's hands move down his face slightly before the reflection starts to move them. Also, the mole that Ethan has on his left cheek isn't reversed in the mirror image. The "mirror" was actually a hole in the wall between two identical sets (one mirrored), with Simon Pegg and a Tom Cruise double in the foreground, and the mask actor and Tom Cruise in the background "mirror" set. (00:57:20)
Answer: This plan is not discussed because they may not have had the hacking skills to take control of the robotic arm. Regardless of whether or not they did, it would not have been the best idea as they are supposed to be infiltrating the facility in complete secrecy. The plan of Ethan holding his breath underwater and manually planting the cards into the system is a lengthier plan, but is less likely to result in them being caught.
Casual Person