Ballad still allows the BLM to DPS harder than with Requiem due to allowing Flare to be used more frequently. For Wanderer's Palace Speed Runs (for ease of numbers I'm not counting AF/UI, spell speed gear or abilities that can only be used once per pull that both rotations would see equal gains from (swiftcast Flares basically)):
Over 2 BLM rotations:
With Ballad up: Fire3>Flare>Bliz3>Fire3>Flare>Bliz3 will produce 1400 potency of damage in 22 seconds. In that time 9 Wide Volleys will produce 792 potency of damage. That's 2192 potency over 9 GCD's (243 potency per GCD). 2192 potency in 22 seconds is roughly 100 potency per second. The BLM needed to cast 6 times.
With Requiem up: Fire3>Flare>Tpose>Bliz2>Bliz2>Fire3>Fire2>Flare>Tpose>Bliz2>Bliz2 will produce 1679 potency of damage in 28 seconds. In that time you could get about 10 Wide Volleys and 1 Rain of Death off for 1200 potency of damage. That's 2879 potency over 11 GCD's (261 potency per GCD). 2889 potency in 28 seconds is roughly 102 potency per second. The BLM needed to cast 11 times.
What we see here is that Ballad allows for the BLM to deal about the same damage in less casts leading to faster kill speed overall. If both rotations were to go for similar lengths Ballad would pull ahead. Once we factor in Skill Speed and Umbral Ice/Astral Fire Ballad will pull ahead even more due to needing to cast more Fire II's under Requiem and Astral Fire greatly favoring higher potency spells. Under Astral Fire we see Fire II getting 180 potency (80 increase) versus 468 potency for Flare (208 increase). (I'm going to go over the math again now that I have more time to include AF and UI bonuses/restrictions)
Additional benefits to this are that it allows a tank to spam Flash to maintain hate without question and allows a WHM to cast Holy in between Cure's without the need to look at their MP. It should be noted that with more Flares being cast you will be generating more enmity which does indeed require the tank to be using Flash on cooldown. With Ballad already applied you save an additional 3 seconds between pulls as well.
tl;dr: In WPSR with BRD & BLM, BRD should full time Ballad (outside of boss fights, Requiem for boss fights), BLM should cast Fire3>Flare>Bliz3 (repeat) for the best DPS. Ballad also allows Flash and Holy spam.