Nobody is saying NOT to DPS ever. The problem is that some segment of players believe that a non-DPS'ing healer is somehow lazy, when the only way that can be true is by having the Tank play perfectly, every time.
I'll repeat several other things I've said that people appear to have glossed over, maybe not in this thread
1. There is no such thing as a DPS-check or a heal-check. These are established by the minimum ilevel. If you can enter the instance than the instance can be completed in the role assigned at the minimum ilevel. There are points in the game, where you can buy more time if the healer DPS's, but that's about the extent of any benefit to be had by the healer DPS'ing. In all cases, one screw up by the tank or the healer, and it's a wipe if the healer is doing DPS at the expense of healing. It just requires you to not play poorly to get through it at low ilevel's. Once at least one character is over geared (typically the tank) it becomes a faceroll and players who don't want to play properly get carried by those that can. Which inevitably is the Tank or Healer.
2. No, nobody is saying never DPS, otherwise you don't get through the solo content. The fact is that the solo-content never requires you to heal as a healer, and what little there is under the Conjurer/WHM storyline, suffers from "stupid AI" syndrome. There are FATE's where you can actually use your healing to buy more time by healing things like crates or the NPC's, but since you can't party them, and the NPC's just regenerate in ones that don't fail if the NPC dies, it's faster to just DPS the content. The healer is at a disadvantage in all FATE content because their DPS is weak and slow for the big booms. There's been entire FATE's that 20 DPS players can burn down a boss before you even get to switch into or out of healer, and if you try to DPS as healer, unless you were there first, or there is a collectable solution you're not going to be able to kill things enough to count as a large contributor. That is one of those annoying issues prevalent to using FATE's for doing the Zodiac weapon. When that content is new, the FATE's often dead before you even get a chance to do anything.
3. Yoshi-P has made his intentions clear with the WHM. We will still have to wait for what this entails for the SCH and AST. When I play WHM, all I'm doing is healing and watching enmity. There is no time to "netflix" or read things on another screen without playing poorly by overhealing. For SCH, the pet is much smarter than "cast regen" and the SCH role is a hybrid DPS/Healer. Hence the DoT's are worth far more, and correctly timing shields for damage migitation is the name of the play style. A lot of this has to do with how fast mana burns down between WHM and SCH. A WHM will exhaust all their mana quickly by playing poorly, or by throwing out DPS that is inconsequential when a party-flattener is coming up.
Like the strategy on trash is different for the strategy used for single-boss, and different for multi-boss/boss+with+adds as a healer. For a Tank and DPS it isn't. If there is >1 enemy, you should not have time to single-target DPS, at least your tank and one DPS is likely getting their face eaten if you "do nothing", and if you heal before the tank grabs enmity, you become all the adds targets. When there is a single boss, and you've learned it's pattern, it's much easier to get away with DPS on a healer because you know when you're going to have the opening for it.
That said, clearly the game mechanics thus far do not encourage healing enough, let alone properly. The closer the content gets to face-roll territory, the more you get people demanding tanks and healers to DPS, when maybe they don't want to, or don't have the time/mana for it. Not everyone is going to know the content, and the standard fare from the Duty Finder is that on average half the people don't know the content and the other half don't know they can do X as a Y.
Things change over time, as I've stated with the "regen" issue. At the beginning of V2.0 tanks would just outright curse you out for using it, so my play style has been to avoid using regen unless the character has a debuff that can't be cleaned by esuna. Otherwise using it before the tank has taken any damage results in all the monsters heading straight for you, and tanks have stated they will "let the healer tank" if they do this. Apparently the "lazy healer" trope is a result of the healer blowing all their HoT's and then doing effectively nothing. Or in otherwords punishing the tank for your bad play style. I'm sure the good tanks recognize bad healers, and good healers recognize bad tanks because their roles when played correctly are easy, and when one or the other are playing poorly, it's twice as much work for the other.
When the shoe is on the other foot, the tank thinks the healer is lazy, so they quit using tank stance, and thus now the healer has to heal more than would otherwise be necessary.
Like I've said I've been on the forums a long time and the thing that never changes is the insistent that "someone isn't pulling their weight" , some people have families, jobs and other responsibilities that will never allow them the time to play some of the hardest content because this perverted elitist attitude a small but loud section of players have that "someone isn't pulling their weight, so I'm going to make it harder for them". You know instead of maybe being polite.