Aren't you proving the point that it's nuanced?
Thread seems to be saying LLMs are great because they do the dirty work and leave the fun work to humans. The counter-point is not exactly that LLMs aren't capable of doing dirty-work, it's that the nature of work isn't going to split so cleanly.
And cooking is a good example. Cooking is work. And slop. And it's also incredibly rewarding and creative, if you want it to be. Robots can help along that entire journey.
Maybe this is the core point: "cooking is a solved problem" that's how engineers always think. Except it's not. And 100% automation is still not going to break that discussion so cleanly.