Gaider once mentioned in an interview about the friendship/rivalries something to the effect that how many players, when going with the friendship path with Merrill and enabling her behaviour in the game, were shocked that in this path they couldn't really confront Merrill about what she was doing. And that it just baffled him why people would think enabling Merrill's behavior would in the end help her. For me, it captured for me the difficulty with both the mechanics and perception of the rivalry system as it was probably one of the most complex representation of the relationships in RPGs so far, being done with very little to base it on. In addition for allowing that dichtomy, it was also unique to each character. With Aveline, it represented how she struggled with had she made a difference in Kirkwall. With Varric, it was who Hawke was, was s/he someone to admire or despise. With Fenris, it was someone struggling with their rage and how Hawke dealt with that.The previous approval system, which made it's return in DAI, was simplistic to the extreme, where approval is good and disapproval is bad, with no real opportunity to challenge companions on anything.
It needs to be repeated that I don't think the rivalry system was perfect, for example the comparison you mentioned is a great point on how it sometimes causes that what moment, There's was the color issue, which Bioware has admitted being a mistake, and the fact that there was really little introduction within the game itself to the system. But I am so sad that they moved away from it in DAI and probably are going to stay away, as while having issues, the rivalry system showed promise for me and you could see how it could be improved, while DAI kind of showed for me how ultimately limited the approval system. Especially after having played the rivalry system.
I've wondered for awhile now if an updated Rivalry system might benefit from including the sort of reputation mechanic that gave ME3 players non-P/R influence that aided in those persuasion checks.
Call it, I don't know, 'Respect'- similar to approval, but encompassing both Friendship and Rivalry paths.
Respect is basically the 'reputation' idea of ME3- colorless points that don't change the balance of Friendship/Rivalry, but make the pool bigger (or smaller) as you gain or lose it.
Respect goes up with approval and things that the character likes, but also with Rivalry actions- they may not agree with you, but they can respect your difference of opinion. Respect can go up for accomplishing minor missions (respect for your abilities), and for providing the sort justifications for your decisions that the character respects- ie, Morrigan doesn't like charity, but could respect benevolent self-interest if you point out that you stand to gain from it.
Respect goes down with outright disapproval- hurting both Friendship and Rivalry meters, because now you're doing things they consider actively bad, rather than principled disagreement. Returning to the Morrigan example, giving charity but asking for nothing in return would lose respect. Losing respect is harder than earning it (just by proving your abilities and power by completing tasks you'd be bringing in lots of Respect points), and would normally come from either how you justify a decision (making emotional appeals to someone who wants reasoned justifications) or doing something they see no redeeming merit in whatsoever (ie, resorting to bloodmagic).
Friendship/Rivalry and Respect/Disrespect would often overlap (Morrigan would Friendship and Respect selfishness and personal advantage- the classic 'approve'), but they could also go in different directions. Morrigan would gain rivalry from charity regardless, but the dialogue justication would determine whether you gained respect (benevolent self-interest) or lost it (you're a fool).
On a friendship front, friendship wouldn't always go hand-in-hand with respect either: taking a position a character lies, but for the wrong reasons/wrong means, could allow that ideological/personal agreement even as it costs something as well. Consider the case of Blackwall- breaking him out could increase your friendship if you were already on that path, but your reasons for doing so- but you reasons for doing so (saying something like 'you're my friend' rather than 'you've earned redemption') could lose respect. He likes you, but also feels let down by you. Another example of friendship not equaling approval would be, say, Casandra and reforming the Chantry. Casandra likes reforms (Friendship) as opposed to thinking nothing needs to change (Rivalry), but she doesn't approve of reckless/radical reforming that risk tearing the Chantry apart in the process (Disrespect).
So, in summary- Respect/disrespect works in parallel to Friendship/Rivalry.
Friendship and Rivalry represent how the characters feel about you from those Big (and little) Decisions in which the player makes a stand on something the character cares about. The character has three balances- they either like you, rival you, or can't make up their minds about you.
Respect is how emotionally invested the Companion is in the PC. Strong respect ties into good feelings, even if the player disagrees as a rival. Low or negative respect is what ties into outright dislike.
That's a rough sketch of the concept. Why bother, though? What's the advantage?
-Tying in 'Respect' de-links 'Rivalry' from 'things I hate' and broader friendship (the concept, not the category) from 'sycophantically agreeing with me.' A friend/close companion isn't someone who just agrees, and a rival isn't the same as a child killer just because they both do things you don't agree with.
-Friendship/Rivaly and Approval/Disapproval no longer need to be a limiting zero-sum. Zero-sum morality systems, where extremes are mutually exclusive (think DA2's implementation of F/R, or ME2's P/R) suffer when player is locked out of content for not being extreme enough. By tying strength of emotion to a different stat (respect), now a zero-sum Friendship/Rivalry system can serve as a better barometer of what sort of feelings the NPC has.
-Gating by Respect can not only allows F/R balance to determine tone rather than access (avoiding the zero-sum trap), but can also help pace companion arc content. As Respect is intended to be accrued across the game even by completing non-controversial non-Friend/Rival missions, this would allow gradual opening that isn't strictly plot-tied.
-Respect would also be a good means to allow romances other than pure F/R: you may be mixed enough that a companion doesn't have a strong agreement/disagreement, but you're still close. The archetypical 'we don't always agree, but-'
On the other hand, there are some costs to trying something like that. Just to recognize what I'm thinking isn't so easy...
Increased word budget costs. Approval/disapproval has a simplicity in that the companions hate you, or not. Friendship/Rivalry had two parallel companion/romance arcs. A Respect F/R system could add even more- Friendship, Rivalry, Middling, and still need a few more scenes for outright disrespect.
A (lack of) character antagonism. Depending on how you set up the respect system, getting outright hated could be hard- if Respect points are too easy (such as every mission), then character opinion will rise. This isn't necessarily a bad thing- Bioware frequently has canonical friends of sorts- but it'd be hard to have a scene like Cassandra being drunk and denouncing the player if respect rolls up for anything and everything. It'd be like trying to get a low-EMS score in ME3- possible, but difficult if you play most the content.
Coding complexities. Having two systems, that interact, influence things would no doubt be asking for trouble. Logic checks would have to be checking two different values (F/R and Respect), while needing to track previous conversation types in case you switch F/R or lose Respect and go back below a threshhold.
(Still) needing some re-balancing of the F/R system while you're at it. DA2 had some mechanics for emphasizing F/R division, such as gifts that gave F or R points depending on your path. That would still be useful, especially for mitigating the middling route requirements.
Getting hated would be hard
Three relationship balances
Need non-respect gates of some sort.