I think a girl from the MC's world wouldn't really add anything to the story or dynamic. Much of the conflict in the story comes from the culture clash between the MC and the girls. The MC comes from a world where science has reigned supreme. All the girls come from worlds where that is not the case. Even Blair, coming from a world that might be considered close to the MC's world in the sense of technology and engineering, still struggles with concepts like electricity and energy not coming from crystals.
Much of the conflict resolution in the stories has come from everyone trying to learn more about each others worlds as they try to find some way out of the house. Each of them brings a new perspective which has been useful in some sort of way. You can see this best when the MC is able to use scientific principles to understand a concept of magic. Even if Cait or Rae don't understand the Doppler Effect, the fact that the MC is able to use that to understand magic more is beneficial because its another problem solved.
But it's not just about magic, by travelling to his world and theirs for a time, they're able to resolve some matters for their own sakes. Lyriel and Naomi are able to inform their loved ones that they are safe. Caitlyn is able to explain things to the headmaster and might be able to get some help. Yona is getting her 80s movie montage training and learning to temper her temper. Blair is able to learn more engineering and starting to think of concepts outside of her own narrow worldview. And Rae is seemingly able to start making some amends for her past.
They all are. Lyriel is starting to pull her head out of her ass, moving out of being an elven teenager and maturing into a young woman. Cait is in the process of learning not to leaping before she's looked at something (the girl is sweet and all, but if she were in the MC's world, I seriously get the feeling she'd win a Darwin award). Naomi is struggling to learn that her crew are doing okay without her and that's not a bad thing.
You have all this, so when someone suggests adding a girl from the MC's world, I honestly cannot see her adding anything to the story that hasn't already been said or done. She would just be superfluous to requirements.