"Reactionary healer" =/= "Doesn't plan ahead at all". Freecure procs you simply passively enjoy. It does not inform your playstyle at all. Critting adloquiem is simply something you passively enjoy as well, and perhaps react to by spreading it oppurtunistically.

The probelm with Lillies is that they adjust the cooldowns of your oGCD heals. The purpose of this is to let you use those abilities more often. But for raid fights, you plan cooldowns around certain mechanics.

In order to take advantage of Lillies, you have to adjust your playstyle and play sub-optimally, which is something neither AST or SCH have to do for their core healing abilities. That is the crux of the problem: In Stormblood, WHMs don't gain anything they can skillfully plan for. It is a lowest-common-denominator addition; while SCH and AST get abilities which they can plan for and utillize skillfully.

The core problem, to break it all down to a TL;DR: WHM gains a passive-benefit for 60-70. AST and SCH both gain active utilities which round out their kit and can be utillized reliably and with planning. This means that AST is better than WHM at what they supposedly tried to design WHm to do: Pure healing.