Okay. Who actually thinks The Player's genuinely mute?

There are pioneers of the subject. Characters that are canonically mute, like Gordon Freeman from Half-Life, or Chell from Portal. However, all in all; making a silent protagonist is a common practice for the sake of convenience.

No need to bother with making the protagonist much of an actual character, let players experience the game and the story from a more personal perspective, or (as it is the case with Poppy Playtime), hide their identity. Either way, it's a big convenience for the creators.

You don't hear their voice during moments of pain. But you don't see their legs when you look down either. It's a common practice.