The issue is trying to balance that.
Like, say with your 40% uptime on DPSing you're pushing out 3k DPS. Sounds fine right?
But what happens if you're then able to spend 100% uptime on DPSing because you've taken the spot of a DD class? You're doing what? 6-7k? The same DPS as a DD class, with the extra utility of healing capability if necessary?
It's the same problem with "Tanks doing too much damage". While they're currently doing 5-6k, much more and they'll be competitive with DPS classes 7-8k meaning people will just take additional tanks over squishy DPS.
The flip side is bosses start to be designed with Tank/Healer damage being factored in for enrage timers. Meaning that you then start to get pressured to not perform your role because you need to push out so much DPS in order to get through the encounter.
Which is where my thoughts behind buffs and Stagger came from, ways to make the end goal being to improve party DPS, but in a way that stems from actively playing your role. I.e. Tanks do tank things and stack Enmity (Which could get boosted by "Tank" stats like Tenacity and Vitality), Healers do healer things and heal and support while DD's do DD things and pew pew.
Of course, not to say that pushing out DPS wouldn't also be utilized. I mean, in my example, something like having a boss get Staggered and then people popping DPS cooldowns like Chain Strategem, Foe Requiem, Battle Voice, Brotherhood etc. Then everyone focuses on DPS to capitalize on the additional damage output they can bring for the durations.
So it's not as if personal DPS should become meaningless, but rather, more limited in the scope of the main goal for the role.
But again, healers are the hardest role to try and do this for, because there's only so much you can heal someone (Stacking overhealing/shields also has inherent issues) as well as there needing to be a baseline amount of healing to be done that is achievable the moment you enter the duty (Otherwise, you won't be able to complete it even though you meet all the requirements), so the issue is trying to figure out how to balance their fillers (However much they need to use them).
I suppose one way of addressing them would be to link their DPS skill(s) into their job healing mechanics (Sort of like Cataclysm era WoW where there was talents to make your heals proc damage skills having bonuses and make your damage skills proc healing bonuses. Or, like Warhammer Online's Shaman/Archmage that had Force/Tranquility and uhh... WAAAGH!)
For example, allowing Stone to generate Lilies somehow (Be it RNG, on crits or some other conditional) so they can have more access to their Lilly skills. Perhaps even add in another Lily skill that deals damage (Alongside Assize)
Allowing Ruin/Broil to generate Aetherflow so again, they can have more access to Aetherflow skills and more easily use damaging Aetherflow skills (Perhaps give them a new damaging Aetherflow skill that can deal some nice damage as opposed to well... Energy Drain and its whopping 150 Pot...)
Allowing Malefic to reduce the CD of Draw so they can toss out more cards (They already can get DPS/HPS boosts from Minor Arcana which has a 5s CD already, so they don't necessarily need another skill to allow them to make use of their cards more often. That said, another skill akin to Royal Road to allow them to turn cards into other effects would work well with having more cards to draw, allowing you to enhance, store, turn into minor arcana or this new effect to improve options and diversity with what you do with your cards)
So, in this case, the filler is still going to be damage, however, that filler will still ultimately result in pushing out more healing. Which could be combined with higher AA damage from bosses (Especially if combined with the Tank changes I posited which promote using Tank Stance and stacking defensive stats instead of just STR/DH/Crit) so that this extra healing output feels useful if you're geared enough to be able to get away with DPSing as filler as opposed to using Cure/Benefic/Psychik/Adloquium as filler)