I don't know if the OP's actually against the Friendship/Rivalry system or the writing.
Because I feel those are two separate issues.
The first issue I'll address I'll the system. The Friendship system in DA2 is vastly superior to the old one in DA:O. No longer does your character have to act so out of your roleplaying to keep companions around. There are also valid but different bonus passive abilities added regardless of their opinion, so the game doesn't really reward one more than the other.
And then there's the fact that their status with Hawke changes the intent of their companion missions, their Questioning Belief missions, and their gifts. All of which makes the relationship feel more important.
This is a great improvement. There's still room to continue to work on it, however. It is a great new system that I want to see more of.
The writing is vastly different from Origins. In Origins the companions were companions. They had their personalities and they had things they liked and disliked and they sometimes reacted by walking away. But at the end of the day they were followers and would always be followers.
With DA2 it feels like the writers wished to make the companions more their own people. Isabela will run off with the relic which causes the Qunari uprising. Anders will blow up the Chantry. Sebastien will leave if you don't kill Anders. Carver will join the Templars to find his own path.
They have their own agendas and goals. Some characters (namely Varric) will remain with you no matter what but the others will hang around as long as it suits their needs.
That's more realistic than DA:O but it has an affect on the player, one I think the OP got.
This was not the funny bickering between Morrigan and Allistair in DAO... it seemed like
downright confrontational and bullying at times, especially with regards to how Fenris and Anders speak to Merrill. I get that the issues and tensions in Hawke's storyline are polarizing, and I admire how each character's views inform their identities and storylines, but I think that such extreme dichotomies between group members (and the lack of reconcilliation between said dichotomies over a period of 10 years) is just depressing and somewhat unrealistic.
Because they have stronger characterizations and are not just followers first. It's more realistic (like Morrigan and Sten would ever get along, really) but I can see it annoying players. I was fine with it, I liked that the companions had these stronger personalities and weren't just side characters in a larger tale (Hawke's their side character in many instances).
But it's a valid question. In the commentary for Half-Life 2: Episode 1, the Valve guys talk about how they originally had Alyx more opinionated and forceful, telling the character what to do and where to go. But playtesters, instead of growing fond of Alyx, began to hate her.
They hated her 'bickering' and her constantly pushing them along. Valve discovered that players preferred playing the game when Alyx commented on their actions, rather than directed their actions. And by changing her from active to reactive to the player's actions the testers began to form a positive relationship with Alyx. They began to like her more.
What does that have to do with the DA2 characters? I'm not saying all characters should become more passive and supportive regardless.....but it is an interesting area of discussion.
I love Alyx Vance from the Half-Life games and I love the companions of DA:O and DA2. I don't know what I can offer to this discussion other than showing that it is two separate issues. The system and the writing.