Because traditional time-series modelling (ARIMA, GARCH, ...) is too "simple" and "strict". Just like "simple" computer vision (OpenCV, edge-detection, ...) was crushed by neural networks when having to deal with real world images.
Sometimes you want inductive bias. No universally true claim can be made like this.
This seemed like a good answer at first. But on further thought, images on the whole really do seem to have quite a bit more standard structure / "grammar" to exploit compared to arbitrary time-series. Many images are of the world, where there is gravity so you might see preponderance of blobs at the bottom, or the repetitive types like people, animals, faces, eyes. Wildly abstract images still have some continuity, pixels in a neighborhood are likely to be similar.
Time series in general have none of this kind of structure that's strictly necessary. I'm sure that many real-world sensors typically have some gaussian distribution aspects + noise and/or smoothness and locality types of assumptions that are pretty safe, but presumably that simple stuff is exactly what traditional time-series modelling was exploiting.
Maybe the real question is just what kind of time-series are in the training data, and why do we think whatever implicit structure that is there actually generalizes? I mean, you can see how any training that mixes pictures of dogs and cats with picturing of people could maybe improve drawing hair, detecting hair, or let you draw people AND dogs. It's less clear to me how mixing sensor data / financial data / anything else together could be helpful.