I think the main problem with Ashley is that, in a game about teaming with cool space aliens, most of whom ended up as beloved characters like Garrus and Tali, and exploring a massive galaxy filled with intriguing new worlds, having someone talk about how much aliens suck and we should focus on Earth takes the wind out of the sails
I finally came up with an answer instead of just smugly tiding my way through this thread, and that's Yuzu from Shin Megami Tensei: Devil Survivor.
Yuzu is there to be the Normal Person. She's scared, desperate to escape the demon infested Tokyo Lockdown, and is frequently vocal about that, but people rag on her for these things despite the fact that any person would act like that when trapped in a hellish apocalyptic warzone.
I think the problem with Yuzu, and characters like her, is that they're complaining about the premise of the whole game. We play Devil Survivor because we want to have a fun strategy game where we fight our way through hordes of demons. We're here for a good time, and Yuzu is having none of it, in the same way Ashley in Mass Effect is there to remind us of intergalactic politics when we just want to hang out with Wrex because he's cool and has funny lines.