I think that'd actually be all the more harmful to, especially, the 70+%, as it'd be taking something at least somewhat intuitive (don't GCD heal if you don't need to) and replacing it with optimally wasting heals in cycles to be readied for Cards and, to their caps in preparation for sync with 2-minute damage buffs.
For that reason, though, I 100% agree with that second part. Or at least, I think healing shouldn't prep damage, even though --as a job-unique tool (e.g., Sage, as you said)-- I'd be okay with damage conveying healing so long as it's sufficiently leveragable™.
Going to make the obvious comparison real quick, between a theoretically more damage-based and WoW's damage-based-healer, the Discipline Priest. I cannot stand Disc, mostly because it just doesn't have enough control over its rate of damage for its healing not to feel like a predominantly passive trickle. Imo, if Sage were to go that route, it'd need to be hugely bankable / have really strong control over its rates of damage (and thereby healing).
Ideally, though, I'd also like it to have control over that rate of conversion, too, preferably such that there may --if, say, there were ever content that could offer very threatening but lowish HP mobs to burn down-- a damage-to-healing Sage might have to decide between reducing damage intake by helping to kill the threat that much faster vs. chugging out counter-healing.
(In a lot of ways, if ignoring the constraints of animation for a pipedream-y moment, those 4 nouliths feel like they should be perfect for finding ways to create gradations of healing (many) vs. focusing on damage / resource generation / etc., especially for something like, say, challenging 4-man content.)
This.
Or, to put it another way, the only reason Lillies are flat DPS neutral is because Solace/Rapture takes the place of otherwise oGCD free sources of healing (such as Durochole and Ixochole) on similarly 20s CDs. That's it. To be an otherwise perfect 20s GCD CD mirror of others' 20s oGCD CDs, it needs to refund the lost potency.
Eukrasia-Diagnosis, on the other hand, has no CD. Toxicon is just a copy-pasta EuD-equivalent to Adloquiem's crit bonus additional effect, but through situational AoE potency gains instead of further value awarding more offensive uptime (more generally useful, as long as there's sufficient damage intake to not leave other healing tools on the backburner). It's not meant to be a zero-cost... because it's not a CD.