I'm late to the party, but your post caught my eye. I worry that the premise reads too dystopian for a comedy. How much do you plan to work the details of the premise into the plot?
I once lived in "young workers" housing in France; it was connected to the government somehow though it wasn't cheaper than a regular apartment. It was post-high school to age 28 (technically higher because some guys didn't move out after they aged out), combination college students and young workers. It was one building with cafeteria and a few shared spaces (like laundry, a kitchen residents could cook in, some lounging space). You could rent a room or a small apartment. Anyhow, my experience there was hardly glamorous, but I thought I'd bring it up as an option if you are looking for a less dystopian excuse for young adults living under a shared roof. I could see the Korean government creating some form of housing for young people to counter the challenges young adults face (competitive housing market, difficulty finding full time work, etc.).