[armchairhacker]

"Can you do this without an LLM, using just regular coding?"

LLM to solve math problems, implement API requests, etc. = hard no

LLM to solve challenging constraint problems or statistical problems where we already have a good solution (A*, heuristics, really clever algorithms) = no

LLM to solve challenging problems where we don't have a good solution (medical diagnostics, legalese, manual translation of badly-formatted data) = yes... (people will disagree but if the LLM does these better than a human, it does these better than a human - and if not, the humans will almost definitely benefit from using an LLM)

LLM to do something with natural language, like implement a chatbot, explain something, cheap therapy = hard yes

[qsort]

I agree with your breakdown.

The problem, however, is that your third point is where the vast majority of the potential usefulness of LLM lies, but simultaneously where integration with other systems is highly non-trivial, hence my "calm your proverbial tits" position on the issue.

[loa_in_]

The vast majority of market value maybe, mass adoptability perhaps. But the biggest value is in the fourth point because it doesn't improve a product, these things were basically unavailable until now!