AST's weakness in end game

[AzureFlare]

I don't think they have fewer tools to heal with, all 3 healers share the basic spells needed in this game to heal well.

I agree with your other point though. Having played all 3 healer jobs in Savage (even Noct. AST), I can say the reason that I think people cry about AST is that it is a little more difficult to play. Not because they don't have the tools, but because they have fewer emergency options, meaning you really have to be on point with your healing. Having fewer margins for error doesn't mean a job needs tweaking, it just means the player has to be exceptionally skilled at what they're doing. Pair this with them having stricter MP management, it just boils down to 'you have to be good to do well with a job like AST'. There's nothing wrong with one job being slightly more complex to play than another.

Things I notice from AST:
Assize/Indomitability vs CU/Lightspeed/CO: none of them give instant healing off the global cooldown. Assize/Indomitability are ridiculously easy tools to use, instant and off global cooldown while the worth is about the same if not lower for their AST counterparts when used by average players. That alone doesn't help. Pretty much parallels what you said on 'emergency heals'.
Luminiferous Aether vs Shroud/Fairy: LA can't be used as an 'oh shit'/afterthought while Shroud can and a SCH should generally never care about hate anyway.
CO/TD: Combos combos combos and all over time too. SCH and WHM had much more straight-forward uses of their buttons when combined and I personally feel they don't need nearly as much thought about what buttons to use together like an AST does (given that TD and CO are worthless alone by default). Combine that with a mindset where you generally use a button according to the situation and I can tell why people feel a little freaked out when they have to press 2-3 cooldowns together at regular intervals.

And of course there's more: higher cooldowns, multi-purpose tools, needing to know other jobs and watching their buffs to really get the most out of your cards. There's a lot they can do to make the job more attractive and 'easier' to play, but straight up buffs to the job as a whole? Please no. Most people don't even know the true worth that some cooldowns bring regardless of skill levels, let's wait and see the 3.2 meta first and at most bring Nocturnal's choices on par with Diurnal's.

Oh, and I repeat: 14k mana, 2 non-buffed / 1 extended Ewer, non-CO extended, on a 12 minute fight(? not sure what length I measured it on) or so while using LA+CO on cooldown is pretty much on par with using Assize and Shroud on cooldown. If you don't get that Ewer, use the other cards instead and don't use damage spells. WHM and AST are dangerously close in mana if you give yourself the opportunity to.