Most of the abilities you mention are powerful instant abilities with a long cooldown. My gut instinct is to save those for emergencies. It takes some time to learn when they are safe to use without risking them being on CD when they're needed.

Some WHM specific comments since I've been playing that class a lot recently:

Asylum: With the longest cooldown of all healing abilities aside from Benediction and the requirement for players to stay in the area it's hard to use optimally. Upon reaching Lv70 content a couple of weeks ago I taught myself to use it at the end of every big pull; killing the enemies generally takes long enough that it's ready again for the next pull. At bosses I still use it only sporadically.

Divine Benison: I try to use it for tankbusters but I'm often too distracted to notice the boss cast bar (rearranging the UI might help here). Or I may not remember what the tankbuster for each boss is called since I haven't done too many Lv70 dungeons yet (some of them only once).

Thin Air: I tend to save it for situations where I'm (close to) out of mana and need to do some emergency healing or raises.

Presence of Mind: Used for emergency healing or the occasional DPS burst. Often I just forget it exists because of the long cooldown.

Plenary Indulgence: This one seems to suffers from some design problems. It's supposed to be a followup to Medica (II) or Cure III, but those are powerful enough in themselves that Plenary is often not required. And the confessions usually run out before the next group-wide damage. I do use it occasionally, it's just that I rarely get a good chance to.

Incidentally, my rarest-used skill is probably Cure III. I've been trying to teach myself to use it in grouping situations, but Medica is more versatile thanks to the much bigger radius so I instinctively go for that.