As you point out, BioWare have historically hidden relatively formulaic quest design behind stories and dialogue, and while I'd certainly appreciate a little more actual gameplay variety... I'd honestly be totally fine with a return to that 'hide the fetch quest behind characters, dialogue and a story' status-quo. DA: I's preponderance of essentially story-free filler quests is, as I'm sure came up in the other thread, perhaps its greatest flaw.
In truth, even if DA: I's filler had been somewhat more interesting from a gameplay perspective - as a (terrible) example, say the shards had run away from you, Assassin's Creed-style, leading to a sick parkour display from Inquisitor Ezio - I still don't think I'd have found them as compelling as a series of more formulaic quests that provided me with the opportunity to talk to characters and experience an actual story--particularly if, as is generally the case in the very best side-quests, that story branched and changed depending upon my actions. This is something a decent amount of BioWare's pre-DA: I side-quests, and - to draw the inevitable comparison - quite a few of The Witcher 3's side-quests, did wonderfully.
Environmental storytelling can be good, but DA: I tended to use it in instances where dialogue-and-character-based storytelling would've made more sense. Oh, and the notespam was just awful--there was far too much of it, for one thing, and the notes themselves were almost always utterly uninteresting.
The way TW3 would frequently blur the line between side-quest and main quest, and even side-quest and Witcher contract - you quickly learn in that game that Witcher contracts are by no means always a matter of, 'take contract, track monster, kill monster' - is another idea worth taking some inspiration from, I think.
...
I suppose what I'm saying is, I'd generally rather a quest had a more interesting story - told through character interactions, dialogue trees and so on - than a lot of gameplay variety--though, of course, both would be appreciated in an ideal world.