In deontic logic, we don't tend to collapse everything into "good or bad" but, as you suggest, we have shades of neutrality. The intersection of neutrality and mere-permissibility is not so precise, considering the concepts of supererogation/suberogation: something hyperdeontic is good and permitted but not obligated, and something hypodeontic is bad without being forbidden (impermissible).
Naive utilitarianism, and Kant at his most religious, favor "rigorism," though (everything is good or bad). For utilitarians, the argument is most precisely given in Kai Nielsen's work, I believe, something like:
- It is analytic that doing the right thing is the best thing to do.
- Therefore, the best thing to do is the right thing.
Nielsen seems to have performed a faulty conflation of A → B and B → A inferences, though. For Kant, see Religion within the Limits of Reason Alone, part 1.