A bard has a drastically lower MP pool than a summoner does, as well as their only healing abilities come from their sub job. Summoners' have the most MP of any job, and several blood pacts they can use to help support the party as a healer. Throw in the fact that I'm usually too busy buffing everyone and now pulling, you'd have to be brain dead to think I'd have enough time to be a useful healer.
It is stupid for a SMN to refuse to heal, because there's really nothing else that they're very good at. Their damage blood pacts are pathetic until the level 70 ones, and even then, they get beat by any half-decent DD just auto attacking. I was tanking a party on ninja one time against lesser colbiri(I was 58), with 2 smn's in the party. They claimed that "I'd see the power of SMN," and all they did was do damage pacts, because they got a rdm to heal us. I parsed the party, and I did more than both of their damage combined, without even blade: jin to help me out. So yeah, SMN's job is to sit back and heal, whereas bard's is not.