Encyclopedias exist today as well, and already fit on USB sticks. Still, Britannica has yet to topple the Chinese political system, and ChatGPT will not succeed either.
Modern authoritarian states are extremely adept at controlling the spread of information. LLMs are not even a drop in the bucket for what the state apparatus can do. If sharing USB sticks with LLMs that talk about the Tiananmen massacre ever became popular, you would get USB sticks that talk about how these are Western lies the very next day.