Games are at their most basic level are about the gameplay. Everything else in a game comes secondary to gameplay. So if a character is in someway "ruining" gameplay, that is a very valid reason for hating them. Edge is a good example, as he is literally forced on you.
What you bring up here is a point of semantics. You are making a distinction between the character, and the use of the character. In video games, these to think are inseparable as long at the character in question is playable.
I think they are separable, especially if you're involved in discussions on just characterization/development.
But I do think that it's interesting how mechanics and characters often get mixed up with each other. If a character literally gets in your way from enjoying a game, even if that character isn't bad, it will simply frustrate you. And that general attitude will shape how you view a character. Fair or unfair, it just happens.
Like Tellah from IV, his freaking mp level drove me insane and in the end he started to really annoy me. I was incredibly happy when he got killed off. Or how the hate of Navi came around, she wasn't THAT annoying but the constant HEY LISTEN, which was more a game mechanic than anything else, made her a joke of an entire generation.
It also helps in the opposite way, just look at the way gamers fight over things that aren't even characters, they'll defend weapons or favor certain objects (companion cube) simply because they grow attached it through game mechanics.
EhhHhhh where was I going with this. Probably no where.