Binge watching Forensic Files and this pattern bothers me

I have been off work due to snow for about a week now and I have been binge watching Forensic Files. A pattern I notice that really bothers me, in several different episodes the killer will claim they had “consensual sex” with a victim before the killing. I feel like that is so extremely unlikely in all of these cases that a victim would just randomly have sex with a stranger or loose acquaintance, why don’t they just fess up to the SA since they already got caught as the killer?

I guess what bothers me it’s like they already killed someone, it just adds insult to injury to claim the person wanted to have sex with them willingly.

Is it because the killer doesn’t want additional charges? Or because they can’t admit to themselves or anyone else that no one wants to willingly sleep with them? Or do you think something else?