I haven't finished DA:I yet, so I can't yet comment on the full picture.
However! Seeing as I recently replayed DA:O, I feel compelled to point out something: Using DA:O as an example done well is really strange to me.
+ For one, you bribed your companions to give you approval via gifts instead of any organic relationship progression. (You can argue that you didn't have to do this, but in general you only earned a few plus points with your story decisions, could still earn massive disapproval points which were hard to earn back -- while the gifts gave you a solid +40 alltogether.)
+ Second, in about 85% of all protag-companion talks, there was no organic conversation. Instead, you interviewed them on their backstory. They practically never asked you questions (with the exeption of Wynne) in return. Instead, you ask a question and then get a long tale of backstory. That's it, that's your DA:O relationship building right here. Sure, you know more infomation about them, but it's an uninteresting and impersonal dynamic.
+ Third, because it was so difficult to earn approval points outside of gifts+romance, you were highly encouraged to metagame. Take DA2: You can gain a MASSIVE amount of points with Anders, so losing a few by, say, turning him down? Not a big deal. If it's not a big deal, you can actually roleplay and pick the options that are in character for your protag and see where you end up. In DA:O, if you lose 10 points and you know Alistair needs 75+ points to have his hardening conversation which you need for the ending you're going for... well, you're gonna think a lot more carefully about how much your in character reaction will set you back vs. simple metagaming and agreeing with everyone about everything. 10 points in DA:O weren't that easy to earn back outside of the first gifts or a romance.
I like some of DA:O's characters, but in-game they don't really feel like they have a soul. I generally have to try hard if I want to imagine that my DA:O protag has an emotional bond with them. They have a lot of potential, sure, but believable friendship? Not so much.
DA2 felt a lot more organic: Conversations between Hawke+companion were, in general, an actual back-and-forth organic conversation. The rivalry system didn't always make complete sense but it was a nice way to customise your protag and actually have the companions treat different protags differently. No need for metagaming, too. It also had scenes where you found companions interacting with each other when you arrived! That was really neat. Honestly, I know DA2 gets a lot of hate, but its companion system is just so much better than DA:O.
So far DA:I seems to do okay for conversations that have the zoomed in cutscene!camera. Not so much for zoomed out interviews.
Anyway, point being: You're definitely entitled to your opinion, but I object to the idea that DA:O relationships had more soul. 