♡ — when did they realize this was a convenient exchange 🤔🤔 (I still owe you that ask about them 😭😭)
i think it was never so much of an immediate realization as it was things building over the years.
because karin has had zero sense of stability in her life, light provided that for her. as a classmate, as a 'friend', as a boyfriend (whether openly or behind someone's back) and as much as she disliked having to admit it : she needed that stability more than she knew. karin was always a girl fighting against the world and as university came to a close, the world was getting bigger and heavier and becoming a fight she might actually lose. light had an outstretched hand and she took it.
additionally, her relationship to light (and by extension, his family) provides her with some knowledge of social cues & behaviours. while brilliant, karin is a slew of negative traits that we've all heard time and time again. cruel , blunt , driven , cold - things that often prevented her from gaining the necessary connections she needed to get into certain positions. to put it another way , light (by a mix of having a very rigid perspective of how one is supposed to act and well . . . nepotism) could help her get into places that the orphaned daughter of a violent felon couldn't have gotten access to otherwise. she'll never turn down nepotism baby.
i think, and this is possibly overstepping a tad, karin helps light's image as well. she is smart, she is pretty, she is talented. but she is also from a background that could not be more different than light's. one day i'd like to explore it, but the realization that karin is nothing like him in a home life & what better way to solidify that than by continuing this relationship and showing others just how much better it is for her / ‘saving’ something or whatever he likes 2 call it these days. [ you tell me though , i always over step ]
& it's important to note that karin doesn't dislike light. i think of all the men in the area, karin as she is right now is best suited towards someone like light & they both know that. their relationship is actually fairly smooth and they fit with one another quite well. they understand one another fairly well. karin isn't an idiot, she's aware he was / is kira in verses where it's relevant and she didn't need or ask for any confirmation. , her synesthesia tipped her off the moment he spoke first and perhaps it's selfish, but karin wants him around for her own observation. it's fascinating to her.
karin also just doesn't tolerate light's shit and it's great (to her) that she doesn't have to explain it. there's an underlying understanding in their relationship and that really is to not play her for the fool. she's not, she's got no problem locking him outside of his own home while she sits inside if he wants to play games. i don't think she's ever had to fight for light's 'respect' (at least not openly) & (to her) that's something that was convenient to her. not having to frighten a man into respecting her saves her so much time.
at the end of the day, both of them see an inherent value in the other. while i wouldn't go so far as to say karin 'loves' light in the traditional sense of the word (while she loves various aspects of him, and quite possibly would have 'loved' him if she hadn't become so detached / indifferent / averse to any emotion outside of curiosity, disgust anger etc) , she certainly respects him and that's probably much more valuable in their relationship.