But when people talk about an Origin, they're specifically asking for something detached from the main plot. I'm just addressing the topic as posed.
I would like a combination of an origin and ArcadiaGrey's idea of later bringing in a personal quest that continues the origin narrative.
I would also have liked that each background automatically had one of the dialogue perks by default and we had to "buy" the rest. Nobility knowledge for human warrior/rogue, arcane knowledge for any mage, history knowledge for Dalish warrior/rogue, and underworld knowledge for dwarves and Vashoth warrior/rogue.
No. I greatly prefer the DAI method and was able to RP perfectly well, in fact, the most out of any of the DA games. I like having bare bones information about my character and their background, leaving me to have whatever headcanon I want. I felt too constrained by all of the DAO and DA2 origins, the established families, and so on.
I don't like this either, to be honest. Or well... I suppose it depends on how it's presented. I do NOT want some person popping up that my PC is supposed to care about, or anything of that sort.
For me, it would be ideal to base such selections on player/character input. For example, a Trevelyan can state the kind of relationship they have with their parents during that Josephine dialogue. If the succeeding family quest could be based on the player's dialogue choice, that would be great. Imagine that there are two base quests, one for a good relationship and one for a bad one, and the player is given the one based on the relationship they selected.
To me, though, it makes the PC exist in a vacuum. We have a brief conversation which defines our relationship to our background (and that's still a limited amount of options, we can't upload a written background) and that's the extent of our connection to the world prior to the game.
This can work in games where other characters don't have as much detail to them or established relationships, but in Bioware games it's harder. When we ask Cassandra about Nevarra or Seekers, or IB about the Qun, I want to be able to react based on our background. Maybe the Vashoth is interested in the Qun or abhors it, maybe a mage Trevelyan wants to learn more about Mortalitasi or a warrior Trevelyan about Seekers.
The good example in game is when mage Trevelyan speaks with Vivienne about the Ostwick Circle. There needed to be more of these instances in conversation. I think any Trevelyan should have been able to speak to Blackwall about being a Marcher, for example.