"No, what makes AST a Healer I already readily defined - it is the only one of the five (since I'm including RDM; I suppose we could include SMN and some others in here, too) that has consistent and ready access to heals (up to 5 in total, to be exact, and the only AOE one that can be used at one's discretion with no prior DPS spell required first or as part of it), and it also has the lightest direct damage kit and the only kit that does not require melee range attacks on enemies, or, indeed, any enemies around AT ALL to produce effective healing."

You can define a "healer" however you want, you can also play any of the healing jobs however you want in PVP now, your degree of success may vary- but you do you. I disagree with your definition, I would say that each of the healing jobs is a viable support job in its own way, and each of them as such is designed to provide various types of CC, DPS and heals based upon the fact that each job has its own heals , and can sometimes provide party heals, mitigation or buffs as well. Not to mention that as a healer, depending upon the content you may be the squishiest and most targeted person in the party given DR (looking at FL) - so casting a heal on a specific party member like the old mode is less useful than your CC/damage/ party utility on any healer.