I'm not one who likes to play the role of a healer due to the gameplay model involved. Playing Health Bar Whack-a-Mole is not fun, which is still the way that Holy Priests in World of Warcraft work. Discipline Priests, however, are about to again return to prominence due to changes in Legion that restore much of the utility this specialization had in Mists of Pandaria. In short, this is the way healing gameplay has to be for healers to become more than a distinct minority: you do damage to your foes, through which you heal your allies.
Bellular Gaming put out a video demonstrating the Discipline Priest in action. You really ought to look into this if you're interested in either game design or World of Warcraft, because (a) he's a game designer himself and (b) quite the player (focused on a Marksmanship Hunter for now).
Notice the model here: you are intended to focus upon actively contributing to burning down your group's targets, through which you passive do your job of keeping the group up; your direct heals are supplementary to your usage of the Atonement mechanic. That's how you get players interested in playing a healer.