Here's a topic that I've been wanting to address for a long time now, because I think it's important to differentiate between the "silent protagonist" and the "blank slate" and to understand why this distinction is important to recognize in any piece of fiction. I'm using Link in this instance, because I believe he's the one character that's debated the most with regards to this topic.
First, I want to clarify what a blank slate is. A common misconception is that blank slates are necessarily mute or silent. This is not true—see Alice Liddell, the MC from Mystic Messenger, and Mickey Mouse for examples. In order for a character to fulfill the trope, they must have no actual backstory or experiences, established beliefs or opinions (especially without the influence of player choices in games), and will only really gain any sort of insight as the story goes on.
But even then, they don't actually change as far as character development goes, regardless of whether they have something of a personality. In the case of video games, it's here where characterization is completely up to the player.
Now, does Link fulfill the trope? Let's take a look. There's lore in the Zelda universe that every single incarnation of Link is an intrinsic part of, each being the bearer of the Triforce of Courage. Beyond that, virtually every Link has established relationships with other characters, most notably hometown friends and family members. It's not often that you get to make dialogue choices in these games, but much of Link's life and implied insight are projected through other characters. He starts off as an unsung hero who becomes acknowledged by the people he meets overtime.
Based on all this, the more appropriate label for him would be "flexible slate." This means that good portion of his personality and growth are left to the player's imagination, but just enough of him limits the player's freedom to create their own lore for the character.
What's more, Link has various likes (animals, milk, music, etc.) dislikes (losing companions, ill-intentioned people, etc.) and hobbies (particularly where player skill testing and rewards are concerned) in practically all these games. He shows compassion, anger, fear, sadness, apathy, courage, determination, and even his mischievous side (even more so when it's the player's choice) in countless instances throughout the franchise. He's put through traumatic and stressful situations (Majora's Mask's plot being a great example of this), and makes friends in the process. Why? Because he puts others before himself, and has the patience for it, despite everything he endures. These feelings may not always be explained, but they are certainly expressed or at the very least could be inferred while we're directly experiencing them.
The key idea to take away from all this is imagining what he may be feeling and going through due to your own feelings and experiences. I've always felt an emotional attachment to Link, both as a character in his own right and as someone through whom I can see his world and connect it to my own life. His characterization is brilliant, because all his incarnations have this rich history behind them, nearly all of which with clear personalities shown through expressions and actions.
Even if the early ones that don't necessarily show it, their heroic deeds still count, while simultaneously being someone all players can access and relate to. Just because he doesn't talk, it doesn't mean he doesn't express his opinions through what he does and shows through facial expressions. He doesn't go about saving the world with the intention of making a name for himself—he's trying his best to make other people's lives easier, safer, and happier, both through the main goals and side quests. This isn't stuff a blank slate would do willingly—this is what a person with a pure heart who knows what it's like to go through hardships in their life would do.
In Ocarina of Time, Zelda gave him the chance to relive his lost years with his knowledge in tow, so he could warn her family of Ganondorf's scheme and put a stop to it right then and there. You can tell she felt horrible that he had to skip what were supposed to be the greatest years of his life for it —and he wasn't even doing any of this for some kind of reward. Zelda, who is also pure of heart, saw his own purity and knew he deserves a good life just like everyone else. This is because Link is someone we all want to see be happy.
If he were truly a blank slate, would we really care as much about what happens to him?