I'd say LLMs are not necessarily an indicator that we're close to AGI, but they're also not a non-indicator. Certaintly more of an indicator of it than the invention of the steam engine was. For narrowly intelligent systems, they're getting quite advanced. We're not there yet, but I worry that the moment we actually step into the zone of general intelligence might not be as obvious as one would think.
However, I also don't think there's any basis to make the absolute claim that LLMs will never lead there, because nobody could possibly know that with that degree of certainty.
And yeah, there are multiple ways to screw things up even with narrowly intelligent AI - we don't need AGI for that.