One word.
Responsibility
I, myself, do heals. But mainly because playing dps means having to rely on a bunch of yolo puggys to throw bubbles and off heals. Cause of course they're all dps, even the Sorcs. And god forbid they do anything off spec like keep the team alive after they e aggroed the whole room with overload and force storm. Edit: talking mainly tacticals since I've been leveling all through dble XP and and now sick of dps pugs)
Also leveling is designed around dps primarily. It goes faster if you dps. Tanking and healing through solo content is slower.