I ask whether you found the repeating of the shard, astrological puzzle and one-line fetch quests to be enjoyable?
The way you phrase it, it's as though that's entirely what was given. I would not be ecstatic about a game that is constituted of puzzles and deliveries, but that's not the way it is in DAI. Unless you go out of your way to complete a zone, those quests occur intermittently between major quests (story/companion/etc..).
While going out to hunt crafting materials after acquiring a new party member, one can help that woman find her ring or something. Why not? The next main quest is available if I wish to pursue it.
Those sidequests (not the requisitions though) are there to provide some content in the open world setting. They're there to drive the player and give some context to the exploration aspect of the game. They serve their purpose. Beautiful environments are nice, but that's all they are in the end. You can fill the zones with major story content, but that's way too expensive to do in terms of money and time.
Of course one can simply not care about exploration. That's fine really, but in that case you are choosing to ignore a major aspect of the game. It's your prerogative, so receiving less content is a direct result of your choice to not explore. You still receive a significant amount of story/companion/zone quests that amount to the same amount of time to other BioWare games. (12 main quests, 12 companion quests, 10 zone quest lines, 12 dragons to slay etc...).
Moreover, can I ask whether you could conceive of a situation where dropping say two of those large sandbox environments in favour of hand crafting some more story related content might have benefitted the game in a way that would have made you enjoy it more?
Theoretically speaking, I don't. I will always prefer more content over more environments.
(It's why I loved DA2. I could not give one fig that it was all in Kirkwall and that the maps were all similar. I loved the story. )
It doesn't work that way though.
If you care for some reading, David Gaider posts a lengthy post (broken down to several pages) on how game writing works here.
Basically, they already use up their word budget when developing the actual content of the game ( again, the main / companion / significant dialogue / zone quests), while using what's left to create the ambient quests/dialogue. The word budget is important, as all content is produced as a result of that word budget. You cannot just add to it haphazardly. Quest designs, animations, cutscenes, etc... result from the writing.
David Gaider states that each companion uses up to 2000 lines of dialogue on average. (Even more apparently)
He also says that each main quest around half of that (you must account for permutations and combinations of the quest line).
You say each mini-quest requires 1 line. You'd need 2000 of those miniquests to make up for one companion, even more for the main quests. Hell, that's not even a good analogy because you don't have to design (up to) 2000 animations for each line, record each of them, and have them assigned and tested. Those sidequests have only a camera zoom and a voice recording.
So as you can see, those side quests are as big as they can be within the constraints of the game development.