For me complete privacy is a must-have for an LLM that gets access to pretty much all my data (mails, calendar, location, browser history, chats, address book, health, app use, ...).
But there are other benefits such as the availability, even when your phone is offline, latency and no cost per use.
But you are already giving Google, Apple, and/or Microsoft all that data anyway.
I'm not. Are you?
Lower latency, which can be useful for live translation or keyboard autocomplete