What they lack is a reliance on cooldowns to push HPS, that is the WHMs 'unique' strength. A WHM can get caught flat footed and still keep up with virtually anything this game throws at a party right now without a single cooldown thanks to Cure III. AST and SCH can't.
Again, I question your raiding experience and I would really love for you to link your actual character's lodestone rather than hiding behind an alt.
I appreciate your views, but the numbers you're basing them on simply don't add up and it really strikes me as a case of 'the grass is greener on the other side' syndrome TBH.