Shin Megami Tensei, a series that popularised ‘monster taming’ in video games, makes good use of dialogue trees to expand on their protagonists and create a flowing story that the player has some control over. It’s highly imersive in the hands of a skiller writer who knows their audience, and the development from Persona 3 to 4, and Devil Survivor to Devil Survivor 2, shows that they are still improving.
Even without dialogue trees there are ways of navigating a story-driven experience without dialogue. Simple “yes” and “no” answers can be enough if the side characters and events are interesting enough. Pokemon and Shin Megami Tensei are both successful franchises that have never relied on player character dialogue to win fans.
A silent protagonist’s charm is in their nature as “blank slates” for the player to project themselves onto, so that events don’t happen to the character, but to the player.
And there are times when silence is best, anyway. When your best friend sacrifices your other friend to summon the god of solitude he calls “Noah”, it’s probably for the best that your character can’t tell him he’s an idiot.
Whatever words you’re given, they won’t be as theraputic as the words you choose yourself when you’re remorsely beating him into dust later.