I do think this would be a nice addition.
As you said, while writing those out you already create part of their stories and it makes things more realistic.
Also it would be nice to just have some more background information for each sims visible. I often rotate and then I sometimes forget what I had in mind for them. Or when going through the household manager, It would be nice to have more overview of what each sims in there is about. I'm thinking it could also include occupations and highest skills and such.