I've always disliked when the relationship causes everything else in the story to grind to a halt. When nothing else is happening the characters just interact in a static vacuum or, at best, a series of disconnected set pieces. I think it's more interesting to see a relationship develop in a dynamic and relevant context, especially because it's a chance to show how the characters handle external influences together.

In a similar vein, I dislike when characters become irrelevant when they aren't part of the main romantic plot. Just because two characters aren't actively trying to bone doesn't mean their interactions lack meaning. A lot of VNs fall prey to this, where characters effectively vanish if you aren't following their path.

You might be surprised, but I'll actually say that a lot of games have good character chemistry. Maybe not proportionally to the total volume of video games out there, but at the very least enough that I can fill my time with games of this sort. And I'd also add that many of them can have this chemistry only because they are video games and respond to your inputs in some way. The various small, comfy interactions in Hollow Knight, for example, exist only because of characters responding to you performing non-contextual actions around them, leading to a certain scene involving a little bench in a very rainy city.

But the one that felt the most meaningful? Or the most impactful? I don't know, I really don't know, I feel that whatever one I'd choose I could argue for it being a bad candidate in comparison with some other option.

Now, the second part of that is a lot easier. Bioware party members. Characters that are thrust upon you and you are forced to... endure... no matter how bad they get or how little reason you have to keep them around. The worst of them being the gay creep from DA2, a character that is not only unpleasant in his own right, but also has the worst romance writing in all of Bioware's games. Not only because he's an absolute asshole, but if you happen to have a character that can romance him, it turns really uncomfortable on top of that.

The character is called Anders if I remember right b.t.w. While most of the characters in Dragon Age romance kinda like planks and as such are easy to ignore, Anders is not. He's more like a creepier, male and gay version of Aerie, which I think is a reference frame you should be familiar with. Though unlike Aerie he has no redeeming qualities nor a particularly good reason to be the way he is.