It worked in Origins because we had excellent characters both good guys/gals and bad to distract us from the practically fairytale plot. The characters made the story.
Hm, I don't agree on these excellent characters in Origins. Bioware imo created some very nice characters for Mass Effect and compared to that, the character writing in the Dragon Age series is just lacking. Maybe that had something to do with the "wooden" presentation and technical execution of Origins but that's probably not the only reason. I think Dragon Age's characters are caught between Baldur's Gate and Mass Effect and they have a hard stand there. Bioware cut back text and therefore the possibility of depth and complexity of the characters (coming from BG2) but they also never reached the presentation and emotional engagement of the Mass Effect series. Dragon Age is somewhere in between and as a kind of hybrid (which is not only true for story and characters but almost for every other aspect of the game, e.g. combat) it's hard for it to rise above in something. While you can argue that Mass Effect was mainly a "bro story" of all too likeable characters Bioware at least achieved in making them memorable, even in a cheesy way but that's better than nothing. Imo they didn't achieve the same with any Dragon Age character.
Another problem is that Bioware's typical story pattern has become too worn out and overused imo. It gets harder and harder to overlook and excuse that obvious weakness with every new game they release with the same basic story patern, no matter which characters they put into the game.
One major flaw of storytelling and character design in newer Bioware games is imo that they are always centered around the main character as "the most important person in universe". That's imho never a good starting point for complex and realistic storytelling. Of course it's also not that enjoyable to play someone who isn't important or meaningful at all but this one guy who has to save the world story limits possiblities and complexity of storytelling. If you start your story that way there is of course little space for inventing companions in another way than just "help the hero to save the world". That worked for Mass Effect because Bioware managed to emotionally engage players by good presentation, well done player agency and just (over-)likeable characters that gave the whole thing the style of a "road (or better spaceship) movie" (I guess that's one of the core reasons why so many people were angry about the end of ME3, breaking that kind of atmosphere the rest of the series was built upon). But I think Bioware never reached the same emotional engagement with Dragon Age causing players to overlook the structural weaknesses of storytelling...
But of course that's not only Bioware's failure but an industry wide problem. One of the main issues here is hyper-sensationalism. The danger in games have to be bigger and more deadly in each new game. You can't even just save yourself, or your family or just doing your job. Today you have at least save the country, better the whole universe. There is little space for complex human interactions with such a crucial and heroic job to do. It's the hero's journey in its most extreme form without much chance for (human) failure or the exploration of human motives other than how to overcome personal doubts on the way of becoming the world's biggest super hero. Side characters are just side people here bostering the main hero on his way. They are just "used" to enable him to fulfil his task instead of being real characters following an own agenda. These "personal quests" from companions Bioware came up with are no substitute for characters with a real character and agenda. It's only an illusion to give you some emotional engagement in their life without making them complex or deep characters. In the end, their job is to help you to do you job as the heor. I admit that this is a general problem of party-based RPGs but I think Bioware is so experienced in that kind of RPGs that there is little excuse that they haven't improved on the formular since Baldurs Gate. They even dumbed it down by cutting most of characters's depth by cutting most of the text which was used to create deeper characters. You can't achieve the same with some spoken lines of voice acting, especially if your tech is not really suited for that (maybe that's better in Inquisition but Origins was clearly lacking here).
To put it that way, Witcher 2 was a game centered almost completely around characters, which means Geralt AND the main NPCs. Dragon Age instead is almost solely centered around the main hero with everyone else only interacting with him instead of interacting with each other or the world itself. I hope Inquisition improves on that (at least they cut Leliana and Morrigan from the companions list so let's see if they can change something here) but I have huge doubts given Bioware's general design vision for the Dragon Age series and their latest track record...