Facts and evidence always are at the core of all arguments, the persuasive thing. The problem with most people is who is speaking. If you are enemy, the things you say are bad.

I suspect that LLMs not being human allows people to not just anthropomorphise the robot, but they project themselves upon it. When someone speaks to the LLM, they're kind of, or actually just literally talking to themselves. But then something new! 'Themselves' suggests new information to themselves. And now without the scary / icky meat and blood human on the other side, said person accepts the argument on its own merits.

Of course, the concern now is arguments based on false or statistically hacked data.