Later on a bard gets a finisher which can heal. I use that in PVP quite frequently. I do my normal song that leeches health and gives to raid building up points then click the finisher for the bigger heal.
Yah, but you can't always have it up to 5 combo points when the tank needs it most. You can use the ability "Rift" to give you 5 combo points if it doesn't miss since "Rift" is still considered an attack. But you can only use this ability once every 3 minutes.
You can later pop "Virtuoso" as an ability and spam for 15 seconds any of your bard finishers which includes Coda of Restoration. This is an oh shit button and if you can't take down in 15 seconds what you need to, then your are screwed after the 15 seconds like you would have been before.
Bards are NOT main healers for a group. They are a support soul only. Now, if you have 2 or three bards in a group, you may not need a main healer from the sheer collective combined HOT power that adding multiple bards can do.
Bards in groups are primarily designed to make everyone else do what they do better. Tanks can tank better. Healers can heal better with less stress. DPS can dish out more damage. This is the power of the bard class. On top of this you add a bit of healing and possibly some decent DPS as well. It is literally the only "jack of all trades, master of none" soul in this game. It is not the best healer, it is not the best dps, it can't tank really, and it is not exactly the best buffer (archon is better than bard with permanent toggle buffs instead).
However, what the bard does well is give a little of everything to a group to shore up any weaknesses. A good bard in a good group will allow that group to plow through content it couldn't do before. I know as I am speaking from first hand knowledge. Also, there are plenty of really bad bards out there that simply do not know how the class works in groups. I am talking 40+ bards as well as the lower level ones.
For example, I was in a group with another rogue, we both had bard setups and tank setups. I switched over to tank and he stayed bard. It was getting ROUGH because he almost never kept up his buffs, his heals and dps were really bad, and it was just not going good.
So we switched as I am an excellent bard. It was smooth sailing from there then on, even if he was even crappier at tanking than me. At least I knew how to hold AOE agro all the time as a riftstalker and could keep my shields up. He didn't, but that didn't matter. Because I was the better bard, the group was in far less danger when something slipped past his agro to beat on someone else, or if he forgot to use his finisher to put up his defenses in a timely manner.