I feel like they've lost the plot with the whole "lets Rank up Milly" thing. We know the dungeon is dangerous, and that they try to restrict access by rank as a safety measure in response to such horrible tragedies as the one MC lived through. Milly is not a competent adventurer yet. She has potential, but so far is still just learning how to exist in the dungeon at all, and would 100% die on the first level if she didn't have someone like MC to look after her. But now they want to get her a Rank she doesn't deserve in order to go deeper into the dungeon where she doesn't belong and would very possibly get killed?

TL;DR: Milly shouldn't go deeper into the dungeon until she's at least competent at the 1st floor, and its weird that MC is trying to get around fool the safety measures to do so, especially given his backstory.