Just to toss in a quick 2 cents:
- I used to heal in WoW as well (druid, priest, paladin), and I agree that addons helped a lot in that game
- I've picked up healing in this game as well (AST so far but I plan to do them all)
- It was a small jolt not having addons, but admittedly I'm at a point where I don't feel I need them now

Because the general healing gameplay is SO different here in FFXIV from WoW, namely the difference in there being constant rapid-fire shifts in battle and damage, that not having that constant roller coaster has made it so that I don't even feel the need for addons anymore.

I tried macros at one point but even that felt clunky in comparison to simply clicking characters when needed for specific spells. Some other folks mentioned this but at higher levels, most of the big healing events have AOE-based spells to handle and those are a breeze to position and fire off. Plus the UI is SUPER customizable so it's easy to set things up to make clicking an easy, smooth process.

All in all, I'm liking the system here in FFXIV. I'm really enjoying this brand of healing as it has a fun mix of doing small heals, big heals, utility, and dps options (I'm still loving that I have an AOE dps spell!).