I played Fighter type characters all over again, and then switched to bard, and I really loved playing him, even when I was near complete useless in regard to direct damage dealing (didn`t hit, and when hit, didn`t do much damage). But hey, who cares?
I was able to throw some nice buffing spells in (here a cat`s grace, there a bull strength), and keep the fighters up (and I used cure light wands for the job, and only in emergency cases relied on my spells).
When my Use Magic Device rank was high enough, I even throw around some Magic Missiles and protected myself with a wand of shield.
I played the bard from 5th to 11th level and I stopped only because the camaign ended (at least for now).
In another campaign a player decided to play a halfing bard-rogue - no combat abilities expect bardic music buffing, and I believe the player has still much fun. (And yes, he could use sneak attack - if he wouldn`t play the herald`s trumpet during battle.

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But back to the reason why bards can cast healing spells:
Why shouldn`t they? They are Jack of All Trades, right?
And they can`t cast real damaging spells (shout isn`t very powerful...

). He is able to buff the other characters (Diviniation spells, social skills can never substitute a tough fight, but they may avoid the unncessary combats or allow the characters to prepare for them.)
The bard in combat is not to be meant as the focus. That is not his job. He is just there to keep it going on, so later he can report about the "tale of the Krust the Barbarian, Mialee the Wizard, Lidda the rogue". The story of "Elric, the Bard" isn`t meant to be interesting. Talking about yourself becomes boring to listeners. They tend to not believe your stories if they are about yourself.
("Yes, for sure. And then you killed the dragon? With that pitiful rapier, or what? I don`t believe a single word!" VS "Please, tell us the story about Krusk, the Half Orc Barbarian, when he defended the city against the invading orc armies!")
Short: To do his job, the bard does not have to be powerful in combat on its own (expect for his own defense) - but he has to be powerful in support for his comrades. And an important part of this is healing magic.
(And why don`t we hear tales where the heroes are healed by bards? Well, what sounds more impressive, what is the better story: The story about Krusk and Henry slaying two dozens orcs trying to invade the city, or the sory of Krusk and Henry running into two dozens orc, killing 4 of them, running back to the bard who heals them, running back towards the orcs and slaying 5 of them, but dropping Henry on the floor so the bard must come to heal him, then slaying another number of orcs, running back to the bard ... and so on...

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