I see nothing stopping a GM from gathering the facts of Jeffrey Dahmer's life and running a game where the PCs are professional investigators, victims, fans, copy-cats, or whatever the participants want. It can be done seriously or slapstick or sanitised or however you want. You can focus on investigation, or the trauma of the victims' families, or play the various aspects of Dahmer's psyche if that's your jam.
I have no personal interest in any of those things, but they are absolutely gameable in a tabletop RPG sense if you can find two or three people that want to make it so. Even if such a thing would be, as you suggest, "approaching bad taste", that's a subjective call and, more importantly, beside the point anyway. Being in bad taste doesn't prevent something from being done.