Mr. von Karma never adopted me and neither would Detective Badd. Mr. von Karma took me in as his ward. There's a difference. One requires me changing my surname to von Karma and becoming a part of the family and inheritance. The other is the teacher offering the student room and board in exchange for his service.
So, to answer your question: It would never happen, because I never aimed to be a detective. I wanted to be a lawyer. I just simply changed the type of lawyer I wanted to be, because that was what was available to me. Mostly, because technically, I did know Mr. von Karma before Father died, as we did meet up in the Lobby and took interest in him based on how he conducted himself against my father. My father raised me to respect authority and Prosecutors alike. He never spoke illy of Mr. von Karma.
(I'm certain that's why Mr. von Karma never knew I was my father's child. I'm certain he expected father to raise me into believing Prosecutors were foolish, but it couldn't be further from the truth.)