That's not reactivity. The zone quests are not what I,m talking about and those aren't the trade off. The reactivity is in stuff like IB going "ROLF" to you being a Qunari Mage, or all the Dalish specific dialogue options, etc.
In DAO then origins introduced characters and themes that actively contradicted the main story and then completely overruled your character and beliefs to turn it into I
GWs post Ostagar. Then they took it one step further in DA:A when they made it mandatory that you become Warden Commander OR do the ultimate sacrifice.
The backstory was the opposite of meaningful.
Really? The human noble's family being murdered by Arl Howe, motivating them the player to fight against Howe (and Loghain by extension) wasn't meaningful? It didn't add depth to the human noble's story? And besides, characters who knew the noble did react to them on that basis. All the nobles react to the human noble differently to how they react to other Wardens, so it's not like character background based reactivity is a new feature of DAI, it's just handled in a more advanced way. There is no reason why there could not be origins and still have that reactivity. In fact, giving the player a chance to experience the character's backstory could provide even greater opportunities for reactive interactions. Even if there were a trade off and we could only have one of the two, I would still take the Origins over those little additional dialogue moments.
What the origin stories did was provide a background for the character and some potential motivations for wanting to fight the Blight (defend home and family, avenge wrongs done, achieve great things, etc.). Conversely, the Inquisitor is just the wrong guy/gal in the ring place at the wrong time. We know nothing of their background save a single brief paragraph during chargen and are given no reason to initially care who this character is or what they are doing. Other than "The mark is killing you", the Inquisitor has no clear motivation for his/her role in things. If the Inquisitor had more of a backstory, it might provide reasons why the player should be invested in this mission from the outset and inform who the Inquisitor is as a person.
From my own experience, I never really developed any sense for who the Inquisitor was because they lacked the fleshed out background of the Warden and Hawke, and felt comparatively hollow as a result. I never had that issue with any of my Wardens or Hawkes, I always knew who they were because I was able to latch onto facets of their backstory to build that particular character.
As for the issue of overruling the backstory to force the story, the game has to do that to make you play it. The same accusation could be made of Inquisition; the PC might not want to be Inquisitor, but he/she has no more choice in that than the Warden does. The mechanics of the game demand that the character takes part whether they want to or not (you can choose not to play at all, I suppose). The only alternative option would have been a "You run away to Orlais to escape the Blight. Ferelden is destroyed by the Darkspawn. Game Over." screen, which is not very viable from a gameplay perspective since it would make for a short game. Instead, you can rail against the unfairness of being forced to be being a Grey Warden all the while you are playing the game. The game has to make you play it, but it still allows you to play a bitter, unwilling Warden if you so desire.