While that would definitely help, I think it's the emergency healing options that SCH/WHM just have such a better lock on that puts AST so squarely in 3rd place as a healer.

With a WHM/SCH, the group can afford to screw up more times, and when you're pushing progression content, there WILL be screw-ups.

And TBH, even in level 60 dungeons when the group is bad and stands in everything, I've gone OoM on AST just trying to keep people alive.

By design, you cannot indefinitely heal stupid, but SCH can heal stupid a hell of a lot longer than AST can.