I find I get quite a lot of variety simply by adjusting to the situation
If I'm the only healer in a group facing tough challenges I sometimes hang right back, poised for Subterfuge & Confusing Babble, and chuck heals where needed most. I'm a very capable main healer in this mode
More often I melee as a lion throwing heals out as needed, using dot and debuff to speed things along. I can be the only healer in a full group and still operate like this
If we're too well off for healers I can spam DD and DoT and melee with the potential to cast a heal if things go wrong. Nowhere near a full-on dps character but I do seem to outdamage fighters and other priest classes
I'm very effective as a soloer too
Fury is a great class but no you don't always get to decide what you want to do because you should be reacting to what's needed rather than "I wanna spam damage now" or whatever. You can of course not join a group unless there's another healer or whatever but that's a bit self-limiting