The fetch quests actually didn't bother much. They're bound to happen. Any quest can basically be defined as a fetch quest if there's travel from point a to point b and back to point a. I don't hate a quest type just because of the mechanics of it. I don't like them if I don't feel plot oriented ("kill 10 rats" "No, why don't you buy rat some rat poison?"), or like I'm not exploring and instead sent back and forth in a small village a few dozen times (which didn't happen in DA:I). Now I played on nightmare my first playthrough and fetching stuff in the Hinterlands was not necessarily a walk in the park as a low level mage. More often than not a fetch quest would lead to a rift, an interesting landmark/quest or just a generally hard encounter that I enjoyed and the fetching just became secondary.
I also really liked the quests that were not fetch quests, that actually did change the map unlike 90% of other RPGs. It seemed Bioware used the fetch quests (especially the shards) as mechanisms to make sure that a player explores 90% of maps just by doing them so they don't miss out of content. The one zone I didn't feel immersed in was the Exalted Plains, because by that point I had just broken my immersion myself by just finishing extensive fade-touched silverite farm, t3 schematic/material farming etc. and making my character and companions completely OP. The other zones felt a bit stale too because I ran all over them farming materials that they were old. So I took a break and played multiplayer for 2-3 weeks, returned and had a blast finishing up the zones and the last three main plot missions. Much better than my DA2 break which lasted from early until 2 weeks before Inquisition when I finally completed the game. In general I take at least a 3 month break from an RPG as I mod it. 
That said, I believe Bioware missed out on the most compelling quest type that's great for replacing fetch quests. What I like to call the "trap" quest. Baldur's Gate 1 exploration was so fun because you didn't know how encounters were going to play out the first time you did them. They had me so on edge about where I explored that I would ask myself: "Should I really follow this woman to the beach to help out their friend or are they going to turn out to be a vicious Siren that's trying to eat me? Yeah they turned into a Siren and ate me."
That shock of thinking your doing a simple rescue quest only to be lured into an super hard boss fight was great. NPC quest givers were very manipulative in BG1. DA:I I think with all the demons around could have played this up a lot more. Basically the world could have been a big DA:O Harrowing with demons trying to trick and seduce the Inquisitor and NPCs at every turn instead of just hanging around rifts and being a general violent nuisance.
The quest situation would have also been better if things like dynamic player keep sieges (Crestwood Keep and Town being attacked and having to choose which one to save) and better integrated war table missions (like rebuilding things beyond bridges and removing rubble, with war table missions governing patrols, merchants, rebuilding landmarks, smaller forts on maps etc.) weren't cut.