For me, it's not about actions per minute or a rotation per se. From another thread:
The spirit being an interplay between two facets of your kit that creates a risk/reward system and a goal to aim for. For BLM, it's ice vs. fire. For WHM (and healers in general), it's healing vs. damage.
You can be a heal-bot. It's safe. It's cozy. But something in the kit should nudge you towards the idea that, at least for some moments, the best thing you can do to help end combat sooner rather than later is to deal damage yourself.
Not knowing anything about MMOs, I started on CNJ/WHM because my preferred combat style is to win the war of attrition: I'll accept dealing damage more slowly if it means being able to keep the party alive longer/indefinitely. The problem is that in reality, the players themselves start building up stacks of debuffs such as "fatigue" and "impatience." Combined with mostly-scripted damage, what you get is a combat system where healers need to deal damage.
As for why WHM… aesthetics, mainly. Ironically, it is also, in my opinion, the only healer that currently has a damage dealing identity: Holy. Unfortunately, it applies only to trash mobs, but still, it's a subject of memes.