Though you may not have intended it as such, this was written as a blanket statement, rather than one just specific to AS3, especially since you compare it to the whole of 2.0.
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WHM is good for sure, but SCH brings different utility to a raid group. For example, in the last phase there is a cascade that does 14-15k damage every 70 seconds. This is a mechanic that SCH must deal with.
Additionally, SCH dps is better for the split hands because we can use our highest dps ability - bane. Shadowflare also works well here. Selene provides a nice dps increase and eos has insane healing potential (although I only use selene in A3S because our dps was low). This is coming from someone who has cleared A3S.
You are focusing too much on what WHM excel at and must remember SCH is pretty beast in its own right.
If you are perfect with sch tools why you complain? Because you can't have better healing, better burst dps than whm & can't solo heal a fight? Lel.
Sorry, but it seems that played since day one is not enough.
You said a lot of things about SCH that is really wrong anyway. If you think whm is better than SCH during A3S fight, play whm/whm then. I don't think it will be better like that.
You should look at what SCH really brings during this fight than just compare with WHM utility. You're not alone, you should think synergy with your partner instead of thinking about this.