Link being silent is only a construct of the gameplay mechanics, not an actual character attribute. There are various indications within the games that he actually does speak—it's just that we aren't shown what he says.

I don't necessarily see him as being the most talkative sort, considering he usually lives alone and tends to react to things rather than initiating them, but it would fall completely flat to force a live action version of him to never speak. In my experience with the world of Zelda fanfic, most of those who write him as silent tend to be unable to conceive of how to convincingly adapt the gameplay into a realistic depiction of the characters and setting. (There are exceptions, of course; I've seen it done well before, but it's extremely difficult to pull off.)

The Zelda games are hardly the only ones to use the 'silent main character' device, anyway.

A few years ago I spent a lot of time writing a story based on Twilight Princess, and in it I depicted Link as being both soft-spoken and generally disinclined to engage in lengthy conversations, but perfectly capable of expressing himself well when he needs to.