I agree that the scoobies kind of have to simplify everything in order to do their jobs. I even agree that they had no idea about the possibility of vampires not killing humans and subsisting on animal blood when Jesse was turned. Only Giles would have had any experience with magic at that point, and like someone else said, his watcher training (and his background in evil magic) certainly never presented magic as an option for rehabilitating vamps. You're right about the Initiative, too. I mean, at some point, taking creatures off the street and trying to alter their nature does become ethically questionable. But none of that means that we, the audience, can't see the gray area there and wonder. The tragedy of Jesse's death seems to be that it happened so early. Had he been a major character for much longer, the gang probably could have done something to at least try to save him.
I read a fan fiction once that sort of dealt with this issue. Not with Jesse, though. In the fan fiction, Buffy had kids. Drusilla turned up as, like, the scariest villain imaginable and seduced and turned the grown son. As the folks with the most experience in such matters, Angel and Spike tried to rehabilitate the son, but, tragically, he was a lost cause. In the story, the son was still himself, but he was sort of like you might expect a mental patient to be (depending on the condition). Without a soul, every minor childhood issue sort of sprang loose from its confines and mushroomed into a giant issue. Questions about why his mother remained young and beautiful and sexually attractive (in this story, she did come back "wrong" -- as in, immortal) bloomed into sexual desire, which completely freaked him out as well as Buffy. He also became paranoid, convinced that everyone was out to get him. He knew right from wrong on an intellectual level - because he remembered it - but he couldn't reconcile that with his ravenous appetite for human blood. Trying to live as he had before drove him more and more insane. He was twitchy and on edge all the time, especially on routine errands like a trip to the mall. Eventually, Drusilla came to collect her new boy, and the two of them went on a killing spree. I don't remember how it ended, but I'm pretty sure that Buffy had to kill her own son and Spike had to kill Dru (Angel, meanwhile was romancing Buffy's other kid, a girl, which was another level of creepy).
It was a disturbing story, but it was an interesting take on the idea of rehabilitating vampires. The story seemed to suggest that you can't make a vampire change, especially not right away. It seemed to say that time and magic and fate are all required and, also, that being a vamp is no picnic for the person still trapped inside and dealing with all of these foreign and evil urges.
If I could remember the name of the story, I'd post a link, but it's been a long time since I read it. Sorry about that.