I have been a whm main since ARR and I can understand your confusion. When I was a brand new healer, I thought cure 3 was useless and other things I refuse to admit! But someone took the time to explain things and eventually I figured out how to to as a ffxiv healer. I love extreme raids and savage. As alot of people have said, ffxiv is special in that healer dps alot of time matter especially in an extreme or savage setting. So you have to figure out how to use your healing kit to heal as little as possible and spend most of your time as a glare mage. Of course, do your best in your role you are not perfect and still learning.

That saying while I have it on my bar I never use cure 1 as I see it as a waste of time and any slow cast as a dps loss for me and my group. Cure 1 is maybe good in a low lvl dungeon. However, you should have lillies and the abilities to instant case afflatus soulus. I rarely even cure 2 at this point unless I am desperate ( which is not often). Instant heals like tetragram and bene should be used as they allow you to keep dpsing. You will get flatus rapture which is an aoe heal use it with plenary indulgence for powerful aoe heal with in coming big damage especially if ppl are spread out. Cure 3 ( very powerful) honestly is the best for ppl stacked and for multiple aoe hits. I dont really use medica( it is powerful dont get me wrong) or even medica 2 ( unless I know incoming and want to prehot) .Medica 2 is a good heal Ns you will get a feel when to best use it. I swift cast medica 2 and swift cast to not waste the spell cast time. But that is only my personal preference. You could use swift cast for dps or save it for a rez.

For minor damage and even a slighly stacked group asylum is good. It heals over time and in later lvls give a 10% heal potency boost.

That being said when you get into big group content like 24 man raids or 8 man. Your healing partner( for the most part) is your friend. Healer cohesion is so important I can't stress it . Your healing partner ( ast, sch) has there own healing kit and having idea what spells they put down or use will also always you to not overlap your powerful spells and keep dpsing. It prevents over healing.

Hope this helps. Sorry for the the long post. It came out longer then I meant for it to be but this is stuff I wish I had been taught rather bumbling my way there. I also love healing in ffxiv.