I can assure you that anyone who touches numerical simulations of any kind (physicists, engineers, chemists, biophysicts...etc) has tried their hand at ML based surrogate models in the last 5 years, so it's not like they aren't being tested. From my experience, they aren't very robust. Weather modeling is actually one of the very few areas where it seems to work half decently.
Why does it work for weather at all? Is there something that the mathematical models are over-simulating? Is weather easier to predict than we thought? Just curious what the intuition is to regarding the success of ML weather modelling...