Not going to be any time soon... possibly never if collective human intelligence, data, and wealth collapses to the point where you are unable to continue to grow and maintain these AI systems. But the growth of AI naturally will result in a significant decline in human intelligence (known as the "brain rot" phenomenon already starting to take shape). The only exception would be if the AI systems grow quick enough such that they can bear enough burden to assume these responsibilities and maintain all of this themselves. However, the current state of AI is not even close to this...regardless of what certain execs trying to get their AI company to IPO have to say.
Beyond this "intelligence" breaking point, there is also a climate breaking point..... AI is expensive and consumes a lot of resources at the moment.
So yes, we could experience societal and population collapse early - but AI may not prevail either.
AI mimics how human forecasters do it - identifying trends/correlations + pattern matching - but with a significantly larger context window, parameters, and trained historical data set. No use calculating all those physics equations for such a chaotic system. This approach is very strong at the 500mb level, but it sucks at surface details. Once the hybridization of the ECMWF AIFS is done, it will be a very strong model... the ECMWF, GFS, and GFS "AI" will be put to shame.