That would certainly result in better damage (100 pts or so) for everyone's chants, but it makes it difficult to refresh chants on the fly.
A fully synergized BC wears off in about 6 minutes, whereas at current lvl + items, my chants are about 12 minutes. Generally, when any part of the party is running from area to area, I'll try to hit as many players/mercs/minions with refresh chants as I can, just so they don't wear off in the middle of a fight. If we've started clearing an area, my BC has worn off but my initial round of chants hasn't, I can't refresh anybody. This means almost every party member's damage will drop by about 1000 pts per swing at almost the exact same moment, possibly in the middle of a big fight (happened to me last night in the middle of a pack of champ/unique Unravelers).
Now, if you're constantly refreshing my BC, then it won't be a problem. We can try it that way, and I can just try to keep up with you, but you generally kill/loot/run much, much faster than I do.
Mainly we should be aware of the idiosyncrasy and try not to let it hamstring the party at any critical juncture. If we're prepping to go into a nasty area (Council, Chaos, Ancients, Throne Room, et cetera), we generally huddle up and refresh all cries and chants anyway, so maybe it'll be okay.