Did any of the white mages think to ASK the bards "hey ima be DPSing this can I get a Foe's"

because at least one of them should have started singing at that point

As a main bard, I take a glance at the party list (in 8-man) and only automatically turn on Foe's if there's a caster. If someone asks, sure. But I'm not psychic and I don't know who'll be DPSing or not.

I'm more likely to use it by default in a 24-man raid, though.