Yes. It's not as hard as you think. Each squadmate gets two variables - approval and disapproval. When the choice is picked a certain number is added to the appropriate variable. Similarly to ME1 Paragon/Renegade system for Shepard.
It's not nearly as easy as you think. They have to decide how each character would react to each decision - many of which are very gray - figure out how each one would be weighted, and make sure every character has plenty of opportunities to earn enough points to achieve every supported stage. That's just the design - it does not include development or testing to make sure it works as designed.
A lot of people complained about getting rivalry points for turning down Anders' early flirt attempt in DA2 - even though there were more than enough friendship points available to make up for it. It's incumbent on the developers to make sure the player can still reach relationship point x even if they make certain choices in some areas.
Stages act as indicators for character's relationship with the player. They will be more reserved if they don't really trust you and be more open if they do. For example, a character in a neutral stage will not tell you about his upbringing but will act respectfully. A character in a Dislike stage will address the player accordingly.
They sort of do some of that, anyway. Aria won't talk to Shepard about her past until Shepard gives her the datapad retrieved on the Archangel recruitment mission.
But it sounds like they'd need to write, record, program, test different dialogue lines for some of the interactions for each relationship stage. I'd rather they spend more of the word budget on conversations between squaddies - that was one thing I really like about ME3. James & Garrus having a bragfest, walking in on intercom convos, the guards stationed outside the warroom conversing, lots of conversations to overhear around the Citadel.
And a lot of squadmates can die on SM. What's your point?
I thought those cases were pertinent to a discussion about losing squadmates over ideological differences.
You go to the extreme. That one issue should not cause him to leave, unless, like you said, he is written the way that he will not accept other decisions. In my suggestion, you'll lose, say 120 approval and Wrex will not be best buddies with you. Usually you'll have to have a squadmate disapprove of your actions throughout a good portion of the game to make them leave.
Some characters have *that one issue* for which there is no compromise. In DAO, Wynne & Leliana will attack a Warden who defiles the sacred ashes, and you must fight them to the death (There are some conditions where you can avoid it.) I'd be pretty surprised if a genophage cure was not that one issue for Wrex.
Currently Shepard is idolized by all his squadmates. Liara, Joker and Garrus are forced as best buddies, Anderson as some sort of a father figure... Shepard is always glad to see squadmates and worried about their health (Jacob mission, for example). I don't think it's good.
I'd agree those things are problems - but I'm not sure that an approval / disapproval system would fix it. Shepard was really Bioware's character (rather than the player's) from the beginning, though it became more apparent in each game. Some of the character relationship issues in ME1-3 were unique to the trilogy format. I mean, Alistair was the Warden's best buddy and King candidate in DAO, but I could mostly ignore him.
Regarding romance options, Inquisition seems pretty clear on that with unique icon for amorous lines and a binary choice to pursue relationship or not. I never had a problem of locking in an unwanted romance in Mass Effect either. Maybe it's easier for Male Shepard, don't know.
DA2 did that, too, with icons on the wheel.
I don't think lock-ins are an issue so much as flirting. It's pretty easy to inadvertently flirt with some of the characters, when all you really wanted to do was investigate friendly dialogue with them.