Headcanon:
Link CAN speak, but doesn't a lot of the time. Mostly because they often feel conflicted about what to say, or a guesture, expression or A Look(tm) can express what they want to say far better and far quicker.
@Nine i believe this is actually canon in botw
@monorail having played it, I can confirm that yes, this is indeed canon in botw and also it's kinda adorable ;w;
@Nine link can speak, but he doesn't because otherwise he'll have to explain why he goes into people's houses, breaks all their pots, and picks up all their rupees