MCH might be the most fun class in the game but being dead last in damage sucks. Bard is currently the most parsed class on FFlogs for Deltascape. The top bard is 12% in damage behind the top of the melee DPS classes. Are people bringing Bards because they add something or because they think they add something?
Bards add a lot of stuff, which is why they're still sought after even with their DPS being lower(which is by design). They bring a permanent 2% crit buff to everyone in the group, a 3mins cd 15% Direct hit buff to the party other than themselves and a ~1-2mins cd(depends on mana regen) 3% damage taken increase song in terms of damage buffs, all of which help a lot.
But where they shine is the defensive shit on top of that. They have Palisade which is basically Rampart(20%dmg reduction) on 150secs cd and Minne which is basically Convalescence(20% more healing on target) on 45secs cd(which is super low for something like this, lasts 15secs too). They also have troubadour which depending on the song played when you activate is 15% raid health, 10%mdef or 10%pdef, which is great for all the big aoe phases and shit, especially the very end of V4S. They can also Esuna once every 40secs, although this has very little use in raids, but is nice for dungeons. And finally, they still have TP and MP songs, which are vital for progression to recover from deaths or just for healer mp during the healing intensive phases or when you have to rez a couple of people and shit(especially when these ppl are casters if their lucid dream is down, mp song actually lets them DPS right away instead of being dead weight).
So yeah Bards are pretty great for such a "small" damage loss. They're also basically complete unaffected by mechanics in terms of DPS loss, since they can fire while running(the only thing they still have to cast is Foe Requiem but can easily be planned ahead and it's not up that often).
MCH get some of that utility(Palisade, MP/TP song) and a better version of the damage increase as well as a damage reduction on boss, but overall are a lot worse in support, while not doing more damage.
