dude, her stats says she fucked only 50 times including MC... that's less than once a week for a year in a monogamous relationship. that's hardly nympho level.
if she fucked once everyday, it would mean she lost her virginity less than two month before she was chipped.
anyone starting a new passionate relationship, if they had the opportunity, they would fuck every single day, until the passion decreases or real life creeps in. you would not call them nymphos...
so no, she didn't fuck half the town. she has the highest stats among the girls in the academy though. and she isn't shy about what she wants.
where did you see a white knight ? everyone said she is a slut. xD
not to defend Jade, but if you take a more pragmatic point of view to her situation, she likes sex a lot, she likes MC (at least, she finds him attractive enough), she hates pain and punishment, and if you accept her offer she finds out she loves sex *with MC*. moreover, she signed the contract, so unless she does anything to change her situation, she will receive punishments and pain, and MC is free to touch her sexually anyway. she has to obey him anyway. and as far as she knows, he might abuse his position as she doesn't know him yet.
so it makes sense to proactively make the offer. it's win win for her. nothing to lose, everything to gain.
it's at least interesting that she is the first to realize it and the first make the offer.