I think that's much better cuz if they found out she's a commoner they will bully her to the bone. Plus the Duke also wanted to keep his position and fame so he might think that's the better option.
Bro it aint a spoiler. IT'S LITERALLY stated from the start that she was adopted, but that doesn't mean the high society knows of that. Her being the daughter of a concubine is a cover.
In this chapter (56) they say she’s the daughter of a concubine, is she or is that just the cover for bringing her into the dukes house? What?