Knowing that what I do anyone can do, no matter how well I'll do it, is discouraging. Because then, what is my purpose? What can I say that I'm good at?
That's a deeper question that only you can answer. I can only say that your thinking based on how you phrased it doesn't really lead to happiness in general
In case that would happen - welp, I'm out of job, out of something I went to school and studied for a few years, now without purpose or "real" skills (as LLMs are on the same level as I).
It's interesting that you name those examples, because Lee Sedol, the all-time great Go player, retired shortly after losing to Alpha Go, saying:
"Even if I become the number one, there is an entity that cannot be defeated... losing to AI, in a sense, meant my entire world was collapsing... I could no longer enjoy the game. So I retired." [1, 2]
So for some, yes. It is of course also true that many people derive self-worth and fulfillment from contributing positively to the world, and AI automating the productive work in which they specialize can undermine that.
I am in no way disputing that some people would feel that way because of AI, just as some performing classical musicians felt that way in the advent of the audio recorder.
What I am saying is that (1) I regard this as an unhealthy relationship to creativity (and I accept that this is subjective), and (2) that most people do not feel that way, as can be confirmed by the fact that chess, go, and live music performances are all still very much practiced.
