Well so here is my opinion on the matter, and to give you an idea on my experience healing in this game i have zeta on both healers, raid on sch (t13 progress) and have been healing in this game since release.
So, should a healer DPS if the conditions are available for them to do so? Yes, a big big fat yes. However, as you may see how i phrased the question, it is conditional. The priority is healing over dps.
However, what i dont get are these people who are so vehemtly against this idea that a healer should dps. Even in game, progressing through the healers job quests, it is made abundantly clear to you that, as a healer, you also should be dealing damage when you are able to. The CNJ storyline is all about a healer who wont use any kind of damaging spells, and you, as a fledgling CNJ have to change her mind by showing her, by example, how a healer should dps. The WHM storyline has similar tones, with it also being your responsibility to protect the Black Shroud as a WHM not only through restorative magic, but through damaging spells used against those who seek to harm the Shroud.
The SCH storyline also requires you to harm and kill enemies through damaging spells. And dear lord, that final lvl 50 quest on SCH is the best one in the game.
Hell, even in FF14 lore, the war of the magi was between the WHM of Ampador and the SCH of Nym.
In final coils, as SCH (which i raid on), it is required that you dps.
Should the conditions arise, and you can keep everyone alive, then go ahead an dps, and ignore these people who catagorically state healers should not dps. DPS'ing healers are in the lore of the game, and integral part of the healers storylines and the devs have given us the tools to be able to dps and heal.
But above all else, have fun.
So WHM has 2 AOEs: Blizzard 2 at level 12 (thm crossclass) and Holy at level 45
SCH: Blizzard at level 12 for the same reason, Miasma 2 at level 46 and Shadow Flare at level 50. Also arguably Bane at level 30.
Also, arguably Holy is one of the most powerful skills in the game, not in terms of raw power, but the conbination of high AOE damage and a stun. If the healer was not meant to DPS, i doubt Holy would have been designed like this.