Some math for you!
WD by itself is ~1400/1600ish per target over 21 seconds on a 1 minute cooldown, however! Rouse is also on a 1 minute cool down and pushes WD up to ~2100/2500 per target with my gear, MP free on a 60 second cooldown with a single global cooldown.
To match that a whitemage would need to cast 3 medicas taking ~8 seconds to cast and costing 1116 mp.
In terms of HP per second, over 0 to 20 seconds of AE healing it's actually neck and neck. If the Sch precasts succor and gets use out of that first galvanize then it's pretty much even, if they don't then the whm pulls ahead. If the damage is delivered over multiple hits allowing the sch to get more use out of succor then the whm gets left behind.
So actually no, I disagree with your point about the disparity between whm and sch for AoE healing. Whomever comes out ontop really depends on the situation. Frequent big AE hits favour whm, lots of smaller hits or big bursts of AE spaced out over a minute or more plays to a sch more.
In closing, if you are struggling with AE as sch I can only suggest that you take a tighter rein on your fairies!