The 'silent' protagonist is an approach to make the action more distinctive than the dialogue, which is part of the stylization of the games in how your actions (and not words) effect time. It's not as if Crono doesn't speak, its that the game doesn't list his dialogue. Otherwise, people wouldn't know his name, plan of action, etc. Since you are generally in the lead perspective of the character, its a means of not only reducing chat clutter (esp for people that get bored with rpg conversational text boxes) but also not needing to bother with excessive dialogue that simply isn't needed. Most of what could be said, is generally conveyed through action, or semi-repeated by another character without it actually having been said beforehand.
Personally, I find this method works better in sprites because the sprite animations generally convey emotional action better than polygonal graphics. (stylization) Due to that, I find that it depicts Crono better as the silect protagonist than Serge, giving him a better feel for character. Plus, I think the mood-music works better to this effect as well. Serge on the other hand has a past and regional relationships with people, which is required for the story's setup.
Furthermore, i find that games have an increasing trend in needing dialogue. My thoughts are that Serge is 'silent' because it's another attribute to make him similar to Crono, yet maintain his 'superiority.' Serge has a forced feel of greater characterization because he's meant to be 'better' than Crono and able to do things Crono wasn't. I think a speaking role would've suited Serge better; maybe not one that spoke a lot, but just so enough to not be a 'silent' hero
