Firing people, delivering death notices, assembling a sword, saving random refugees, finding poison, finding garnets, finding scrolls, finding bottles, and so forth were trash filler for the sake of trash filler just as much as DAI's trash filler.
Maybe, but Origin's filler is a hell of a lot less boring than Inquisition's IMO.
Right. At least in Origins we had some cutscenes and dialog that filled in some lore for many of them. The 'find a scroll' one is a good example actually. You talk to the curator in Denerim, she tells you how hard it is to find actual artifacts of Andraste. You go to Haven, find the scroll, return to Denerim and she examines it, gushes about how awesome it is etc.
Even the straight hand-in filler was more interesting in that it set the mood of what was going on around you. Sure you collect 10 lyrium potions, but do you hand them in to the mages templar friend or turn them over to the templars? When you talk to the mage apprentices each one gives some dialog that indicates what sort of apprentice they were. You have the option of having one of your party members tell the widow about her husband, and each companion has a different take on how to handle it. Even quests that were straight hand ins with no dialog turned out to have some effect, maybe in the landsmeet. The Crows assassin quest is an example of this.
In Da2 you find some pantaloons, go to the person marked on your map, right click and hear Hawke verbally throw it in the NPC's face.
In DAI you find a note, go to a specific location, find another note, or maybe a chest or dead body, and done. If you're lucky there will be some flavour text, but don't hold your breath. Often it's just a quest complete message.
At least DAI was a slight improvement over DA2. 
I feel a little bad picking on DA2 at this point. It's like the runt of the litter, always picked on, never given enough food or attention. heh.