If WHM is guilty of anything, it's being an overall bland job.

SCH is a healer, damage dealer, buffer, debuffer, and mitigation job rolled into one.
WHM is a healer, healer, healer, healer, and healer.

SCH has an array of ogcd spells, instant heal, and fairy heals, all of which allows increased versatility, multitasking, and healing-on-the-go.
WHM has heals that all require you to stop and cast, some of which are the longest casts in the game. WHM also doesn't have a mini-healer to help cover for them. WHM suffers the same from high-movements fights as BLM.

Now I play both jobs at endgame so I know each well. When I am on SCH I just feel like I'm bringing much more to my party with my increased toolset. WHM is very limited to what it brings. It's just an overall very bland job. If AST can hold it's own healing and still mesh with SCH, you're going to see people drop WHM until they make the job a little more versatile or interesting (IE, not JUST a healer).