I done every story dungeon in Dawntrail with trusts and never found any issues with them as a healer. Wuk Lamat is practically invincible, Alisaie and whoever the other dps rarely ever stepped in bad so I scarcely needed to heal them.

One thing I’d say though is, especially if you're with trusts, it’s always better to prioritise survival over dps. After all, increased uptime can’t be leveraged if you’re already dead. And since there’s no enrage/dps check in any of the dungeons I can think of besides the final boss of Alexandria, even taking extended periods of downtime is completely fine while you’re learning. I kept dying to the first boss of Origenics with the poison spread mechanic when I done it first time; turns out I was greeding Broil casts too hard and trying to slide cast when I didn’t actually have enough time.

Eventually I decided to stop everything I was doing until I was sure the mechanic was resolved safely, then suddenly I stopped dying and had time to actually think about positioning for more uptime (on the same ability 10000 times lol)

I don’t have much experience playing with trusts as a dps in Dawntrail though, so I can’t say if Urianger/Alphinaud/G’raha are much use as healers / in general