I'm not opposed to npc romances, but I think it's a tough balance to hit right, especially when one or both of the participants are LI's for the PC.
Tali and Garrus was very cute and was suitably subtle and in the background that most people seem to think it's sweet, outside of really hardcore Garrus and Tali romancers. Fenris and Isabela were a briefly mentioned hook-up that most seem to find amusing. Dorian and Bull went the complete opposite direction and got a really big focus for an npc ship, and while it made some people very happy, in the wake of Trespasser it also seems to have left a lot of players feeling a little hurt and baffled at how much importance their LI's alternate relationship got vs their relationship with the Inquisitor.
There's also a question of the relationship dynamics and how people are going to react to them, negatively or positively - again, Bull and Dorian are an example of that, but so are Joker and Edi. I'm neutral on them but I know a lot of people find Joker and Edi kind of skeevy. It's shaky territory and you can't please everyone, so I'd rather any relationships stay enough in the background that the potential for fandom freaking out is minimized.
I like the Garrus and Tali approach, personally. It was very cute and had just enough mentions to make me go 'aw' but didn't seem like it was competing for attention from their romances (which wasn't really a concern for me since I didn't romance either of them, but I can see why it could have bothered people who did.)
as far as non-romance relationships, I agree w/ whoever mentioned wanting companions to not always get along. I don't want them to always find common ground. Tbh taking Fenris and Anders around to hear them bitching at each other non-stop was hilarious, at least it made fighting through the exact same cave system 100 times slightly less tedious (very slightly, but still.)