For BRD, Cure IV, Haste, and status cures are very important reasons to sub WHM over RDM. I played BRD in event settings for years (important admission: I retired BRD when the level cap first rose to 80), and singing songs was only half the job. I, and any good BRD from that era, made extensive use of the status cures and cures from /WHM. I honestly don't know if /SCH is now the better choice these days, to be honest.
And yes, a WHM in an event setting (outside of Abyssea) should have enough support to /SCH comfortably. MP conservation should not be an issue for properly supported, geared, and talented WHMs, and /RDM doesn't come close to offering the same perks as /SCH. Even in the Abyssea age, I generally consider the /SCH or /BLM WHMs to be the ones who know what they're doing, and I'm immediately suspect of any WHM/RDM.