Weather prediction is the realm of relatively well understood differential equations based on physical properties. Where deep learning can play is in inference of what's going on between observations on the map and timeline.
The problem is you need to define "decent spatial and time resolution." We regularly run kilometer-scale global models that eschew convective parameterizations and instead directly simulate those scales of motion. Over smaller domains we run models pushing beyond LES scales.
Deep learning applications in the field haven't come anywhere even _close_ to tackling these niches of the field yet. SOTA DL-based forecasting tools run at quarter-degree resolution, if even that, and the field hasn't even begun to run hierarchical or multi-scale models coupling coarse models to mesoscale or finer-grained. Hell - you'd be hard-pressed to even find mesoscale DL weather simulations in the first place! So it's a big, big stretch to suggest that DL can achieve "the same quality results" when no one has even offered a cursory glance at an AI application bordering on the SOTA in NWP.
