I’m not buying this. Dean absolutely believes Jack can be saved. He may be in denial about it, but you don’t jump in and stop someone from hurting himself like that if you legitimately believe he’s an evil being who will destroy everything.
imagine the first time Totsuka manages to make Mikoto laugh, like legitimately crack up tho, can you imagine how happy & proud of himself Totsuka would be!? And he'll keep bringing it up for the rest of that month, because he has to tell everyone in Homra of this accomplishment/ incredible feat!