While I really liked the friendship/rivalry system, to the point it is my favorite companion system so far, I don't actually really want them to bring it in ME:A for the simple reason that the ME games have never had approval as a constantly changing dynamic variable and thus they have never written their characters from that point of view. While it does simplify the interactions somewhat, the good side it is that they are actually able to include very character specific interactions, for example ParagonShep and Garrus in ME3 and their views on war, which had a lot of nuance when looking at it. Maybe if they moved forward with that kind of interactions, while being able to bring in moments like ME2 loyalty mission decisions in to it more, that would sound really good to me for ME:A.
As a sidenote, I cannot stress how much I dislike the basic approval system as it basically enforces a really simplistic worldview that you cannot disagree with your friends. That if you have a different opinion about something, you can't debate or argue about it, but the other person dislikes you because of it. I understand that it impacts the way the characters are written, for example Blackwall in DAI really wouldn't have worked with the Rivalry system, but some character might have benefitted from it, especially Dorian once his end point is shown would have really been helped by having someone push him on what he really views as important. Although the character interaction would have needed to have been restructured, but still. And Vivienne and Sera felt like characters written for a rivalry system, which I guess is why they are so divisive characters as the player is essentially punished for not agreeing with their very polarizing views.
And as a final point, I have never felt companion interaction system to be more gamelike than in DAI with the removal of the approval bars as it suddenly made me constantly question where I was with them in a very artifical environment as there weren't just small random interactions to gauge that with as in normal life.