There's a 1/6 chance of drawing a Spear in the interval of time that lines up with the point at which you plan to use Luminiferous Aether. Assuming (for the sake of simplicity) that you are not going to simply discard that Spear (because you want to Shuffle it in for a better card, because you'd rather have the Expanded Royal Road effect, or because you don't want to waste your existing Royal Road effect on it), and also that you are not going to pay the enormous opportunity cost of wasting a Royal Road effect on Spearing yourself or of putting Spear into your Spread, that works out to one out of every six LA uses having a 96s cooldown, and the other five having a 120s cooldown.
Which averages out to a 116s cooldown on the skill. It's a largely imaginary difference between an AST using LA and a WHM using SoS.
In addition to that, at this point you're talking about the full, expanded skillset of the AST versus the WHM, whereas this discussion is solely about the baseline, passive qualities of each class that happen when you're only considering standard GCD-based heals. When you start to bring in the card effects, you also have to bring in WHM's full suite of cooldowns, at which point AST starts getting tossed around like a rodeo clown.
No amount of Spears and Ewers the AST uses on themself will begin to make up for Assize, let alone the staggering MP efficiency granted to WHM by Divine Seal, or for that matter, Regen. A better use of your Spear card is honestly to give it to the WHM, so they can get a reduced cooldown on not just Shroud of Saints, but Divine Seal, and Assize, and Asylum, and Eye for an Eye.
It's perfectly valid to consider the entire toolset of a class when you talk about balance, but when the class roles and basic abilities are as similar as they are, it's just as valid to consider their baseline abilities separately from their cooldown suite. AST loses out to WHM and SCH a little bit if you ignore the cooldowns and just focus on the baseline, but they get destroyed if you start to consider everything that each class brings to the table. "Forgetting" about the cards (and the WHM/SCH cooldowns) is putting your thumb on the scale in favour of AST, not selling it short.
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