> …given all the success we've had with LLMs, it's weird that we can't use the exact same tricks with time-series data.

Forecasting works, to a certain degree, quite well when there is actually something to forecast. The fact that it often doesn't work (e.g. there really is no effective predictor of where the S&P 500 will be 3 months from now) might just be because the series really is effectively unpredictable (combinatorial explosion, chaotic complex systems, and all that).