I think LLM's will prove to be useful in any domain where most work happens in front of a computer. As LLM's make programming cheap, they also reduce the cost of building new software that automates work currently performed by humans in other fields.
If you provide best models with all the data and context an average white collar worker has to perform their job, in most cases they will do just fine. But in real world that context is often scattered over multiple systems, or sometimes exists only in people's heads. I believe that's the main bottleneck for adoption now.
This assumes that a significant portion of the average white collar worker’s job is amenable to automation.
But most white collar workers I know spend most their time either talking to each other, or thinking real hard about what to say the next time they get together to talk. If that’s generally true then it would suggest that there isn’t much white collar work that LLMs, which are now widely regarded as exceptionally poor communicators, can do particularly well.
> I think LLM's will prove to be useful in any domain where most work happens in front of a computer.
A lot of that work entails work with very little margin for error and hallucinations.
You're missing the biggest suggestion from the GP's post: that the key to LLM success is verifiability.
Software has high verifiability through compilers, linters, static analysis, leak/memory corruption detection tools, or the very least, running the program to see if it crashes.
Math (as has been making the headlines recently) has high verifiability through automated theorem provers. Notably some of the non-mechanized math results from LLMs have been demonstrated to be wrong (and presumably many more are being checked; these aren't exactly easy to understand proofs).
Game playing (chess, go, Star Craft, etc.) is similarly verifiable: you get your score and you always know how you did in the end (even if not in the moment).
Making assumptions about LLMs in non-veriable domains is making a claim about LLMs that doesn't match their current capabilities. Maybe they'll get there and maybe they won't; I can speculate as well as you can but we're both guessing, so I'm not sure how much value the speculation has.