You're far from being powerless as WHM.
In fact, you can ditch some serious HPS. The main difference with the ASYT is that it as a lot of delayed heal while WHM they are all direct.
The AST shine on the duration while WHM shine by it's straightfowardess and quickness to respond at a unforseen situation.
A good exemple is Alphastice 1.0, when the boss get all the party to 1HP (it's because i did it this WE that this exemple pop up in my mind). Only the WHM can put back everyone between 75% to full HP in a mere 2 buttons (or 3 if swiftcast is up).
It's a relatively low level exemple but, if you look at the WHM kit, everything is done to enhance it's raw and direct Healing.
To sum up, with AST you must plan when and how to use your healing kit (the same with SCH), whith WHM you react directly to the present situation.