I think healer dps is just the inevitable reality of healing downtimes in games which don't actively enforce to be passive in those, like old WoW did with their stand 5 seconds still for mana regen rule, which I think we all can agree was horrible. Where I think it can vary is how much dpsing is actually involved in healing. Holy Priest for example is pretty similar to most ff14 healers, the healing toolkit is mostly there for downtimes and outside of the kyrian covenant ability, which is sadly tossed out in DF, its really something you do inbetween heals. Restoration Shaman feels a bit more aggressive and is bit more maintenance heavy, but mostly the same though it gets some neat boons in Dragonlight, for example causing its ground targeted hot field to also cause damage. In some cases it is heavily involved with the act of healing itself, fistweaver monks, melee holy paladins and discipline priests and in the case of Restoration druids, it is kind of a reward for proper hot management. You have your hots up on the party and their LP are smooth, time to catweave which is kind of a nice minigame inside the class where you get a simplified version of the feral druid toolkit. Fun note on Discipline priest, their dps healer playstyle was actually created because they couldn't balance it being a shield healer well, for the most part it was just too good in reducing incoming damage which frustrated the more reactive healers.
Its actually both and pretty self-contradictory. SE doesn't wants to push high healing uptime because they are afraid it will drive away the casuals which creats high dps uptime which they take into account by adjusting enrage timers with high dps uptime in mind and yet at the same time they don't want to cater towards this high dps uptime playstyle by giving healers more tool because they are afraid that it will make casual healers feel forced to dps. I think it boils down to why I say healers are the role of low expectations: They are designed this way because whoever is responsible for this obviously seems to consider healing more of a chore.part 2
And personally, I would say yes, Healers always should be expected to dps during downtimes. Its basically the only productive thing that you can make them do during inevitable healing downtimes, anything else would just boil down to occupational therapy, especially since healers need dps tools for solo play. I think the differences boil down to how much healers would be pushed to dps and how much it affects their gameplay loop, where you can have varrying degrees. In terms of wow healers, you could have the holy priest who can just push some dps inbetween heals without worrying you much. Then you go a bit further, like restoration druid, where you can chose your dps style and on the extreme you have holy Paladin, who is what Zenos would play if he was a healer.