I don't agree. Eirin's thing has always been her science and doctoring, the bow is a minor sidenote compared to that.
Yeah but the thing is that doctoring and science has always had a certain 'mad scientist' note to it, if this was the TF2 medic then yeah it's perfect, but that doesn't really work given that Mercy is definitely a benevolent good girl (even in fanon). I'd almost go for Byakuren, but she's a lock for Zenyatta so I'm not honestly sure which one I'd use for her.