Arguably it's a good thing that Battle Voice doesn't affect the BRD, because that means you can use it whenever it's best for the party instead of going at lengths to try and sync it with your own rotation (current 180s timer doesn't align with 80s song rotation at all). It's easier to use, less punishing to mistime and overall more flexible as it is. Their DPS balance accounts for it too, so there's really no need to "fix" it.