My main issue with trying to warrant limits onto a specific job on the basis of enough people wanting it across that job's whole role... is that they are two very different levels. We might as well say that across all roles, enough players dislike casting spells that one (existing) Caster shouldn't be allowed to have casts, or that enough players dislike positionals that one (existing) Melee shouldn't be allowed to have positionals...
Perhaps if it were a new job, at least, I'd be less miffed by the idea, but even then, it seems unfair and unnecessary to hold back anyone its appeal to anyone would otherwise want to play with that job's aesthetics and gimmicks to that arbitrary limit, especially when engaging with, say, those positionals would still be only one among myriad optimizations and would be entirely excess to clear requirement anyways for all but certain Ultimates.
On the other note, obviously cognitive load is not actually split into 'healing optimization' and 'damage optimization', and to give such a warrant to say that adding complexity to healing is fine while adding it to damage is not would be... pretty absurd.
However, keep in mind that raising party sustain requirements can come with decreased party DPS requirements, even if only by just buffing healer potency-per-GCD, and the diminishing returns on effort put toward either purpose (not wiping now due to not meeting sustain checks vs. not wiping to enrage from low healer DPS) might have separate and perhaps even different curves (devoting one's attention towards not wiping now may reward one's efforts overall than just slightly making up for the DPS falling behind), so in that sense that fiction/analog can still indirectly have some use.