There are treatments of such combinations available in the literature, e.g. T.V. and Rao[25] covers an approach to AI alignment issues in this vein. I’m not directly following that train in what follows, but I think I should acknowledge that kind of background at the outset of my question.
So, there is a famous, and famously contested, principle that usually goes by the name of “ought implies can,” sometimes this implicitly covers “ought implies might not” and sometimes these implications are kept apart. Whether the raw modal diamond is the kind of “can” at stake is also debated.
Now Kürthy, et al.[22] concludes that though “ought” doesn’t automatically get us to “can,” “must” does get us there by default. This analysis follows upon e.g. the SEP entry on deontic logic, specifically where an ought/must distinction is addressed.
So let’s say that there’s a generalized sense of “to be done” that, when coupled with various temporal quantifications, yields a basis for various deontic operations. We can talk about “to be done once ever,” “to be done once a day,” “to be done every other day,” “to be done more often than not,” “to be done most of the time,” and ultimately “to always be done” vs. “to never be done.” Presumably the forbidding operator FR could be based on “to never be done.” How reliable would it be to base “ought” on something less than “to be done always” and then “must” precisely on the same otherwise? This would be akin to how necessary existence can be “described” as existence-in-all-possible-worlds, and then how “must” is used for that alethic modality (necessity) besides.
Counterexample option: the SEP entry on the concept of evil represents the broad use of “evil” in a way suggestive of “must never.” Yet we also sometimes speak of “necessary evils.” I’d argue that these are rather different senses of “evil,” though with an understandable point of comparison (in abstracto), but I don’t want to go off too much on that tangent for now (maybe in responses to responses, if there are any here…).