Approval directly affects the "get laid" mechanic, but a big part of both franchises is the focus on companions. After all, it affects companions that are unavailable as LI's to the PC just the same. Wrex is about the closest thing we ever got to a companion with approval in ME, and I think that worked out pretty well, I'd say better than the others. I guess the VS counts, but I didn't feel that it was quite as good.
If you're talking about being able to talk Wrex down on Virmire or convince Ashley/Kaidan to trust you during the Citadel Coup, I think these were great steps towards the sort of friendship/affection systems that I'd like to see more of.
The first time I played any of the ME games, it was Mass Effect 3. I know I should have started at the beginning but I just played it on a whim not realising I was going to fall in love with it and then the series as a whole. Anyway, during the Citadel shoot-out, I couldn't talk Kaidan down because my rep was low (no import), I hadn't saved the council (again no import or Genesis 2) or visited him enough in the hospital and I think Vega took the shot and I was horrified but it was amazing too. I had no idea that it was going to happen or that I was or wasn't building up enough affection due to some in-game message.
When I went to play ME1, I didn't know much about Wrex because he wasn't in ME3 but I learned my lesson that if you care about your squad mates, you should talk to them so when it came to the showdown I was able to talk Wrex down even though I didn't have enough rep because I had completed his family armour quest. It was much more satisfying to be rewarded for something I wanted to do for Wrex rather then having an approval system constantly reminding me how Wrex felt about my actions so I felt the need to alter my play style.
Wrex is also a good example of someone who is a good and loyal friend even though we disagreed on so much and were polar opposites personality-wise; a friendly 'rival' if you will without the big red bar filling up to tell me. If I had gone so far as to sabotage the genophage cure however, there would have been no coming back from that no matter how close or loyal a friend he was.
If they could take this approach to all squad mates where they don't just blindly follow you no matter what you do and being at odds with them doesn't necessarily make them any less of a friend yet you can still make decisions that will cause them to turn away from you forever AND make all of this invisible to the player, I will be happy.
edit: BTW I reloaded an old save with Kaidan to 'fix' it, which is shameless meta-gaming I know but it didn't take away the original impact of the scene.