I think the reason why Link doesn't talk, at least in BOTW (Spoilers?) Is because he knows how much of an effect he has on people being such a great knight and doesn't want to have a negative effect on people by what he says. At least that's what I've heard. So I sort of made a headcannon that since he never speaks he's formed a habit of being uncomfortable, embarrassed or even afraid to speak, taking him out of his comfort zone to do so, so he doesn't to keep up the great and fearless knight act and he only talks in private with someone he trusts.