I think Spoekes was referring to how useless the +4 to +9 accuracy is on each piece, rather than healer DPS itself.
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At i130 healers have 412 accuracy (that is assuming they're not using i110 melded accessories or added accuracy to their zodiac relic). Meaning even at the current ilevel cap, healers do not have enough accuracy to hit 100% from the rear in turn 1 which was designed for i70-i90 players (and has an accuracy requirement of 432 from the rear, 20 more than what healers have). And healers are also 103 accuracy below the rear requirement for the final turn, turn 13.
That being said, Scholars possess a few spells that have guaranteed hits (one of these isn't Energy Drain, for some weird reason), meaning their DPS can be fairly consistent as opposed to a White Mage who actually needs accuracy (and luck) to land all of their attack skills. It is not uncommon for me as a White Mage to miss several times in a row. I had Presence of Mind popped and I was trying to get in some DPS and I missed every single attack (RIP 1,000+ MP). So, imo, healers need for accuracy and the lack of it is very annoying and needs to be fixed.
As well they also need to fix the sinkhole of an MP cost that White Mage attack skills are. I understand the higher MP cost of our DoTs, but Stone II costs more than a Cure and is horrifically MP consuming as your hardest hitting attack skill. White Mage can already easily run into enough MP issues if there is a lot of unexpected damage or deaths. Scholars have a much easier time coping with those situations (MP wise anyway).
SCH has generally been more of the DPS choice for high end content... partly because of their skills that can't miss, but there's more to it. Cleric stance lets the fairy heal as normal, and the SCH isn't as bound to GCD -- lustrate is off GCD *and* unaffected by cleric. Basically, SCH retains a lot of healing ability even in cleric and even spending GCDs on DPS.
And... even with 100% hitrate, WHM single target DPS just doesn't compare to SCH (AoE is great though).
But the real reason I'm skeptical healer acc (or DPS mp, etc) will be buffed much was mentioned earlier in the thread. Healer DPS is really more of a meta thing. In order to convince SE to give healers lots of acc, it seems one would need to convince Square Enix to incorporate the meta. One of the reasons that SMN hasn't been buffed further SE stated is that it also buffs SCH DPS (which the changes to Ruin/Ruin II already did).
This may actually be possible, since we are getting new DPS abilities in Heavensward. However... How exactly this will play out, particularly in raiding, remains to be seen.
I can't see much changing, as I said before. That SCHs can DPS as hard as they can now is less a product of SE wanting healers to DPS and more due to underlying game mechanics (because Bio and Bio II do not have an initial hit, they don't check for Accuracy--Shadow Flare is the same but for a different reason) and as Risver mentioned, because of Eos/Selene ability to heal through Cleric Stance. Since so far as we know, WHM and Astrologian won't have anything especially unique in this regard, things will probably be about as they are now in the expansion. WHMs are receiving a spell that deals damage and heals, but it will presumably still check for Accuracy, which suggests it's meant for dungeon runs and FATEs, rather than raid content.