Yeah, purposes like living human life. Very interesting and meaningful endeavor, I highly recommend it. Instead of only restricting yourself to philosophical a-b-c logic, you can live and experience life as well.
>deterministic system is incapable of deterministically outputting a strings that audience members could interpret as referring to a mental state.
What is the point of that conjecture? Are you trying to equate yourself with a deterministic markov-chain generator?
In that case I have even less reason to communicate with you. It's like you have even further proved my point to comparing yourself to it, because it makes the distinction perfectly clear: when someone knows they are talking to a GPT-3, they immediately recognize that there is no reason to keep talking to it. "Free will" is a very good explanation for why people feel that way. They know that some humans have free will, and GPT-3 certainly does not, and they don't feel any reason to talk to anything that does not. You could have some other terms also describing this phenomenon, but free will is a good and useful one.
This is also the reason why people don't spend time talking to GPT-3, other than for 10 minutes as a fun thing. And after 10 minutes it is not even fun anymore.