The problem with your post is that healers are essentially tanks in Frontlines, so which ever one has the best ability to fulfill their specific role (an excellent tank and healer combo) is the one that would widely be considered the best. Scholar may get points for the fairy and various other abilities (E4E, virus), but too many of their skills require parties to be lined up perfectly for them to use, and the vast majority of them do not mitigate enough to make much of a difference. Succor is the exactly the same as Aspected Helios (with the exception of some crits that may happen), but the difference is that AST has a stronger Cure II which has no equivalent on Scholar, the ability to instant-shield (which, on average, is stronger than Adlo), and doesn't have to worry about micro-managing a fairy which runs all over the place.
Plus, AST can buff its healing at any time without sacrifice anything and synastry is great in PvP. Plus a balance on someone with battle fever is ridiculous. If all healers still had the ability to Stance Dance in PvP, I think we'd definitely see a similar instance in PvE where Scholar comes out on top in many instances.
However, you're removing its most vital assets as a class - it IS essentially half DPS, after all. With no cleric stance, what makes SCH shine in PvE is glaringly absent in PvP. It becomes a decent healer with more to handle. If Scholars still had their outstanding DPS capabilities I'd agree with the idea that it could hold the title, but alas, that was severed long ago.
All of this, too, is without even looking at the PvP skills offered (retrogradation OP af).
Besides that, the argument that "AST can't heal as well as the other two" simply isn't using it correctly.
As I stated before, AST is good but definitely not invincible. Anyone who believes it is "invincible" just really doesn't know how to counter an AST properly. It's largely the same for all healers, the difference with AST is that you can't just, as a DPS, spam weak GCD abilities and expect it to die like you can if you're fighting other melee DPS (which is what mostly people bitch about, anyway.)
All resources are finite; the difference is that AST has more in their toolkit for mobile healing and instant heals that make them outlast any Scholar and White Mage when being attacked. With AST, healing instantly is never a problem unless your MP runs out. Unless you have Lustrates or saved your Tetra/Bene, you're going to have a harder time. It's just the way it is.