I fully 100% agree Link has untapped narrative potential, but as a player, the only time his silent avatar-style bothered me (and this is in hindsight) is Skyward Sword. That one felt like he was all but written dialogue and he was flat, but at least no one else had voiceover. That would've made him stand out more than he already does in that game.
I personally like the silent protagonist angle. I understand as the stories get more complex it can't stay like that forever, but I genuinely like projecting myself into that role and kind of look forward to it for every new Zelda game.
Regarding BOTW specifically, I somewhat disagree. Link's insignificance to the plot isn't caused by him being mute IMO. They give him a pretty solid and relatable reason for it in Zelda's diary at the end of BOTW (which the ghost of King Rhoam alludes to at the end of the GP). Link is insignificant to the story because the story doesn't frame any "Hero of Time"-like destiny for him. He's had the Master Sword since he was a child born a prodigy in a family of knights. The sword never reacts to him ever, and he has to prove himself to wield it 100 years later. This even goes in tandem with Zelda not having the physical Triforce to access her sealing magic, the mummy character in the BOTW2 trailer potentially being the 10,000-year-old hero (who, plot twist, is similar to Ganondorf as we know him AND could also wield the Master Sword) from Impa's legend, and the Master Sword itself only ever reacting to Ganon. Link can't hear the voice inside the Sword, Zelda can, etc.
If Link is going to talk, it needs to be done in a tasteful way that doesn't make BOTW2 show up like "oh yeah, Link talks now!" My idea to fix this was to play off the reasoning given in BOTW, and give Link these confessional moments. Zelda also says he never really confides in anyone, so him going to some kind of temple to talk to a sage and unload some of his burdens through the journey could be interesting, give people the Link dialogue they want as a test, and lean the audience into him talking to Zelda or the new Champions. The first game was heavily themed around Zelda finding herself, the second game could give Link a similar treatment.