You don't train the AI with the forecasts made by other systems. You train the AI with the actual weather that was measured hours/days later.

Weather is a complex mix of many systems. The traditional approach is to understand all the systems and add them together. Since we don't understand them all fully, we get a lot of chaos.

The ML algorithm doesn't care about the science, the agendas, the theories, nothing. It just looks for patterns in the data. Instead of an exact calculation it's more akin to numerical analysis. Turns out that looking at the whole in this case, is better than the sum of the parts.

The people who predict the weather are often damned smart and very experienced.

It's the problem that's hard.