What I remember is that a lot of people used the word 'AI', other (including me) said 'thats not intelligence, it's too specific', and poof, a new word came to replace the word AI, 'AGI', to mean an AI that can adapt to new, unforseen situations.

The LLM that will convince me that AGI is near is one that will understand language enough to find the linguistic rules of conlangs they weren't trained on (or more specifically, engineered languages made by linguists with our current knowledge of how languages work), and create grammatically correct sentences. Something someone trained on can do with great effort, but it's more due to breaking habits and limited brainpower than real complexity.

I think that OP's conclusion may be true in a not very meaningful sense: once a particular non-trivial threshold of competence is defined for every task (infinitely many), then any policy must be bad at some of them.