You don't have to dps in most content. Pretty much none of it really. But healing in this game isn't that hard, especially once you have the battles down and know when the hard hits are coming. I get extremely bored if I don't dps, since if every one is doing their job, its just an odd cast here and there. The only times I don't dps is if the group is doing something to annoy me, and at that, i generally don't have the paitence to stop for more than one or two pulls or a boss.
Healing is easy enough that a great healer doesn't only keep the party alive, a mediocre one can do that.
All that being said, if you want to really focus on straight healing AST or WHM is the way to go. At least with AST you can play with cards while you wait.