I don't feel any extra responsibility as a Tank or Healer than Im doing DPS. I've played and loved all 3 roles in every MMO I've played. Many people simply want to do big damage.

Without a Tank, everyone dies.
Without a Healer, everyone dies slowly.
Without DPS, Everyone dies REAAAAAAAAAAAAAALLY slowly.

No job is more important than any one other job. Some phases need more skill for some jobs than others. Look at Siren for example. A good example of a boss where everyone is just as important as everyone else. DPS have to kill zombies, Tank has to keep the hate, and Healers have to keep everyone topped off. A failure from any one role means a wipe.
Titan is another good example of a fight that asks much of all its roles.