ACN pets can't heal. The biggest thing an SCH brings to the party pre-30 is the fairy, who is a good enough healer to solo-heal pre-30 dungeons. An ACN would be hard-pressed to heal on their own in the 25-29 range. An SCH with no fairy would similarly have trouble healing in the 25-29 range, but that's why they have the fairy. And, as pointed out, how would they be stopped from queuing as a healer in post-30 content? Can you imagine an ACN queuing as a healer for, say, WoD just to troll? It would let people queue as healers and then play as DPS, which is bad. As pointed out above, ACNs can't wear healer equipment after a certain point when healer and caster split off. The classes on gear become CNJ/WHM/SCH for healer gear and THM/BLM/ACN/SMN for caster gear. For books, only SCH can wield healer books, and ACN/SMN can wield caster books (apart from the SMN relic, which is SMN only).

Like another said, BLM and PLD can cross-class physic/cure respectively, but would make terrible healers. Allowing ACN to queue as healer in level 50 content but not a PLD to do so too is totally inconsistent. (You can argue that not all THM/BLMs have Physic, but all PLDs must get access to Cure to get their class crystal, so you can't say that not all PLDs have Cure. And, you can change cross-class skills mid-dungeon.)